Business Statistics For Contemporary Decision Making 7th Edition by Black – Test Bank

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Business Statistics For Contemporary Decision Making 7th Edition by Black – Test Bank

Ch06: Chapter 6, Continuous Distributions

 

 

 

True/False

 

 

 

  1. A uniform continuous distribution is also referred to as a rectangular distribution.

 

Ans: True

Response: See section 6.1, The Uniform Distribution

Difficulty: Easy

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. The height of the rectangle depicting a uniform distribution is the probability of each outcome and it same for all of the possible outcomes

 

Ans: False

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution

 

 

 

  1. The area of the rectangle depicting a uniform distribution is always equal to one.

 

Ans: True

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution

 

 

 

  1. Many human characteristics such as height and weight and many measurements such as variables such as household insurance and cost per square foot of rental space are normally distributed.

 

Ans: True

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Normal distribution is a skewed distribution with its tails extending to infinity on either side of the mean.

 

Ans: False

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Since a normal distribution curve extends from minus infinity to plus infinity, the area under the curve is infinity.

 

Ans: False

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. A z-score is the number of standard deviations that a value of a random variable is above or below the mean.

 

Ans: True

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

 

Ans: False

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. A standard normal distribution has a mean of zero and a standard deviation of one.

 

Ans: True

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The standard normal distribution is also called a finite distribution because its mean is zero and standard deviation one, always.

 

Ans: False

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. In a standard normal distribution, if the area under curve to the right of a z-value is 0.10, then the area to the left of the same z-value is -0.10.

 

Ans: False

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Binomial distributions in which the sample sizes are large may be approximated by a Poisson distribution.

 

Ans: False

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

 

  1. A correction for continuity must be made when approximating the binomial distribution problems using a normal distribution.

 

Ans: True

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

 

  1. If arrivals at a bank followed a Poisson distribution, then the time between arrivals would follow a binomial distribution.

 

Ans: False

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. For an exponential distribution, the mean is always equal to its variance.

 

Ans: False

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. The area under the standard normal distribution between -1 and 1 is twice the area between 0 and 1.

 

Ans: True

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

 

Ans: False

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The normal approximation for binomial distribution can be used when n=10 and p=1/5.

 

Ans: False

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

 

  1. For an exponential distribution, the mean is always bigger than its median. .

 

Ans: True

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

Multiple Choice

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the height of this distribution, f(x), is __________________.
  2. a) 1/8
  3. b) 1/4
  4. c) 1/12
  5. d) 1/20
  6. e) 1/24

 

Ans: b

Response: See section 6.1, The Uniform Distribution

Difficulty: Easy

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the mean of this distribution is __________________.
  2. a) 10
  3. b) 20
  4. c) 5
  5. d) 0
  6. e) unknown

 

Ans: a

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the standard deviation of this distribution is __________________.
  2. a) 4.00
  3. b) 1.33
  4. c) 1.15
  5. d) 2.00
  6. e) 1.00

 

Ans: c

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the probability, P(9 £ x £ 11), is __________________.
  2. a) 0.250
  3. b) 0.500
  4. c) 0.333
  5. d) 0.750
  6. e) 1.000

 

Ans: b

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the probability, P(10.0 £ x £ 11.5), is __________________.
  2. a) 0.250
  3. b) 0.333
  4. c) 0.375
  5. d) 0.500
  6. e) 0.750

 

Ans: c

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then the probability, P(13 £ x £ 15), is __________________.
  2. a) 0.250
  3. b) 0.500
  4. c) 0.375
  5. d) 0.000
  6. e) 1.000

 

Ans: d

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then P(x < 7) is __________________.
  2. a) 0.500
  3. b) 0.000
  4. c) 0.375
  5. d) 0.250
  6. e) 1.000

 

Ans: b

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then P(x £ 11) is __________________.
  2. a) 0.750
  3. b) 0.000
  4. c) 0.333
  5. d) 0.500
  6. e) 1.000

 

Ans: a

Response: See section 6.1, The Uniform Distribution

Difficulty: Hard

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x is uniformly distributed over the interval 8 to 12, inclusively (8 £ x £ 12), then P(x ³ 10) is __________________.

 

  1. a) 0.750
  2. b) 0.000
  3. c) 0.333
  4. d) 0.500
  5. e) 0.900

 

Ans: d

Response: See section 6.1, The Uniform Distribution

Difficulty: Hard

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If a continuous random variable x is uniformly distributed over the interval 8 to 12, inclusively, then P(x = exactly 10) is __________________.

 

  1. a) 0.750
  2. b) 0.000
  3. c) 0.333
  4. d) 0.500
  5. e) 0.900

 

Ans: b

Response: See section 6.1, The Uniform Distribution

Difficulty: Hard

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the height of this distribution, f(x), is __________________.
  2. a) 1/10
  3. b) 1/20
  4. c) 1/30
  5. d) 12/50
  6. e) 1/60

 

Ans: a

Response: See section 6.1, The Uniform Distribution

Difficulty: Easy

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the mean of this distribution is __________________.
  2. a) 50
  3. b) 25
  4. c) 10
  5. d) 15
  6. e) 5

 

Ans: b

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the standard deviation of this distribution is __________________.
  2. a) unknown
  3. b) 8.33
  4. c) 0.833
  5. d) 2.89
  6. e) 1.89

 

Ans: d

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the probability that an oil change job is completed in 25 to 28 minutes, inclusively, i.e., P(25 £ x £ 28) is __________________.
  2. a) 0.250
  3. b) 0.500
  4. c) 0.300
  5. d) 0.750
  6. e) 81.000

 

Ans: c

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the probability that an oil change job is completed in 21.75 to 24.25 minutes, inclusively, i.e., P(21.75 £ x £ 24.25) is __________________.
  2. a) 0.250
  3. b) 0.333
  4. c) 0.375
  5. d) 0.000
  6. e) 1.000

 

Ans: a

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the probability that an oil change job is completed in 33 to 35 minutes, inclusively, i.e., P(33 £ x £ 35) is __________________.
  2. a) 0.5080
  3. b) 0.000
  4. c) 0.375
  5. d) 0.200
  6. e) 1.000

 

Ans: b

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the probability that an oil change job is completed in less than 17 minutes, i.e., P(x < 17) is __________________.
  2. a) 0.500
  3. b) 0.300
  4. c) 0.000
  5. d) 0.250
  6. e) 1.000

 

Ans: c

Response: See section 6.1, The Uniform Distribution

Difficulty: Medium

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the probability that an oil change job is completed in less than or equal to 22 minutes, i.e., P(x £ 22) is __________________.
  2. a) 0.200
  3. b) 0.300
  4. c) 0.000
  5. d) 0.250
  6. e) 1.000

 

Ans: a

Response: See section 6.1, The Uniform Distribution

Difficulty: Hard

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 £ x £ 30), then the probability that an oil change job will be completed 24 minutes or more, i.e., P(x ³ 24) is __________________.
  2. a) 0.100
  3. b) 0.000
  4. c) 0.333
  5. d) 0.600
  6. e) 1.000

 

Ans: d

Response: See section 6.1, The Uniform Distribution

Difficulty: Hard

Learning Objective: 6.1: Solve for probabilities in a continuous uniform distribution.

 

 

 

  1. The normal distribution is an example of _______.
  2. a) a discrete distribution
  3. b) a continuous distribution
  4. c) a bimodal distribution
  5. d) an exponential distribution
  6. e) a binomial distribution

 

Ans: b

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The total area underneath any normal curve is equal to _______.
  2. a) the mean
  3. b) one
  4. c) the variance
  5. d) the coefficient of variation
  6. e) the standard deviation

 

Ans: b

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The area to the left of the mean in any normal distribution is equal to _______.
  2. a) the mean
  3. b) 1
  4. c) the variance
  5. d) 0.5
  6. e) -0.5

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. A standard normal distribution has the following characteristics:
  2. a) the mean and the variance are both equal to 1
  3. b) the mean and the variance are both equal to 0
  4. c) the mean is equal to the variance
  5. d) the mean is equal to 0 and the variance is equal to 1
  6. e) the mean is equal to the standard deviation

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. If x is a normal random variable with mean 80 and standard deviation 5, the z-score for x = 88 is ________.
  2. a) 1.8
  3. b) -1.8
  4. c) 1.6
  5. d) -1.6
  6. e) 8.0

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is 3.4. What is x?
  2. a) 63.4
  3. b) 56.6
  4. c) 68.6
  5. d) 53.2
  6. e) 66.8

 

Ans: e

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is -1.3. What is x?
  2. a) 58.7
  3. b) 61.3
  4. c) 62.6
  5. d) 57.4
  6. e) 54.7

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z < 1.3)?
  2. a) 0.4032
  3. b) 0.9032
  4. c) 0.0968
  5. d) 0.3485
  6. e) 0. 5485

 

Ans: b

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(1.3 < z < 2.3)?
  2. a) 0.4032
  3. b) 0.9032
  4. c) 0.4893
  5. d) 0.0861
  6. e) 0.0086

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > 2.4)?
  2. a) 0.4918
  3. b) 0.9918
  4. c) 0.0082
  5. d) 0.4793
  6. e) 0.0820

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z < -2.1)?
  2. a) 0.4821
  3. b) -0.4821
  4. c) 0.9821
  5. d) 0.0179
  6. e) -0.0179

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > -1.1)?
  2. a) 0.36432
  3. b) 0.8643
  4. c) 0.1357
  5. d) -0.1357
  6. e) -0.8643

 

Ans: b

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. What is

P(-2.25 < z < -1.1)?

  1. a) 0.3643
  2. b) 0.8643
  3. c) 0.1235
  4. d) 0.4878
  5. e) 0.5000

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. The 50th percentile of z is ____________.
  2. a) 0.6700
  3. b) -1.254
  4. c) 0.0000
  5. d) 1.2800
  6. e) 0.5000

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. The 75th percentile of z is ____________.
  2. a) 0.6700
  3. b) -1.254
  4. c) 0.0000
  5. d) 1.2800
  6. e) 0.5000

 

Ans: a

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let z be a normal random variable with mean 0 and standard deviation 1. The 90th percentile of z is ____________.
  2. a) 1.645
  3. b) -1.254
  4. c) 1.960
  5. d) 1.280
  6. e) 1.650

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. A z score is the number of __________ that a value is from the mean.
  2. a) variances
  3. b) standard deviations
  4. c) units
  5. d) miles
  6. e) minutes

 

Ans: b

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Within a range of z scores from -1 to +1, you can expect to find _______ per cent of the values in a normal distribution.
  2. a) 95
  3. b) 99
  4. c) 68
  5. d) 34
  6. e) 100

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Within a range of z scores from -2 to +2, you can expect to find _______ per cent of the values in a normal distribution.
  2. a) 95
  3. b) 99
  4. c) 68
  5. d) 34
  6. e) 100

 

Ans: a

Response: See section 6.2, Normal Distribution

Difficulty: Easy

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed.  What is the probability that a randomly selected bulb would last longer than 1150 hours?
  2. a) 0.4987
  3. b) 0.9987
  4. c) 0.0013
  5. d) 0.5013
  6. e) 0.5513

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 1100 hours?
  2. a) 0.4772
  3. b) 0.9772
  4. c) 0.0228
  5. d) 0.5228
  6. e) 0.5513

 

Ans: b

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 940 hours?
  2. a) 0.3849
  3. b) 0.8849
  4. c) 0.1151
  5. d) 0.6151
  6. e) 0.6563

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Medium

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20. Determine the value of x such that 60% of the values are greater than x.
  2. a) 404.5
  3. b) 395.5
  4. c) 405.0
  5. d) 395.0
  6. e) 415.0

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life of at most 30,000 miles?
  2. a) 0.5000
  3. b) 0.4772
  4. c) 0.0228
  5. d) 0.9772
  6. e) 1.0000

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life of at least 50,000 miles?
  2. a) 0.0228
  3. b) 0.9772
  4. c) 0.5000
  5. d) 0.4772
  6. e) 1.0000

 

Ans: a

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?
  2. a) 0.5000
  3. b) 0.4772
  4. c) 0.9544
  5. d) 0.9772
  6. e) 1.0000

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The net profit from a certain investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor will not have a net loss is _____________.
  2. a) 0.4772
  3. b) 0.0228
  4. c) 0.9544
  5. d) 0.9772
  6. e) 1.0000

 

Ans: d

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. The net profit of an investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor’s net gain will be at least $5,000 is _____________.
  2. a) 0.1859
  3. b) 0.3413
  4. c) 0.8413
  5. d) 0.4967
  6. e) 0.5000

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. The probability that the project will be completed within 185 work-days is ______.
  2. a) 0.0668
  3. b) 0.4332
  4. c) 0.5000
  5. d) 0.9332
  6. e) 0.9950

 

Ans: a

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days.
  2. a) 211
  3. b) 207
  4. c) 223
  5. d) 200
  6. e) 250

 

Ans: c

Response: See section 6.2, Normal Distribution

Difficulty: Hard

Learning Objective: 6.2: Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve.

 

 

 

  1. Let x be a binomial random variable with n=20 and p=.8. If we use the normal distribution to approximate probabilities for this, we would use a mean of _______.
  2. a) 20
  3. b) 16
  4. c) 3.2
  5. d) 8
  6. e) 5

 

Ans: b

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Easy

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

 

  1. Let x be a binomial random variable with n=100 and p=.8. If we use the normal distribution to approximate probabilities for this, a correction for continuity should be made. To find the probability of more than 12 successes, we should find _______.
  2. a) P(x>12.5)
  3. b) P(x>12)
  4. c) P(x>11.5)
  5. d) P(x<5)
  6. e) P(x < 12)

 

Ans: a

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Medium

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

 

  1. The exponential distribution is an example of _______.
  2. a) a discrete distribution
  3. b) a continuous distribution
  4. c) a bimodal distribution
  5. d) a normal distribution
  6. e) a symmetrical distribution

 

Ans: b

Response: See section 6.4, Exponential Distribution

Difficulty: Easy

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. For an exponential distribution with a lambda (l) equal to 4, the standard deviation equal to _______.
  2. a) 4
  3. b) 0.5
  4. c) 0.25
  5. d) 1
  6. e) 16

 

Ans: c

Response: See section 6.4, Exponential Distribution

Difficulty: Medium

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. The average time between phone calls arriving at a call center is 30 seconds. Assuming that the time between calls is exponentially distributed, find the probability that more than a minute elapses between calls.
  2. a) 0.135
  3. b) 0.368
  4. c) 0.865
  5. d) 0.607
  6. e) 0.709

 

Ans: a

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. The average time between phone calls arriving at a call center is 30 seconds. Assuming that the time between calls is exponentially distributed, find the probability that less than two minutes elapse between calls.
  2. a) 0.018
  3. b) 0.064
  4. c) 0.936
  5. d) 0.982
  6. e) 1.000

 

Ans: d

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes. Find the probability that a component is assembled in 7 minutes or less?
  2. a) 0.349
  3. b) 0.591
  4. c) 0.286
  5. d) 0.714
  6. e) 0.503

 

Ans: e

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes. Find the probability that a component is assembled in 3 to 7 minutes?
  2. a) 0.5034
  3. b) 0.2592
    c) 0.2442
  4. d) 0.2942
  5. e) 0.5084

 

Ans: c

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. On Saturdays, cars arrive at Sam Schmitt’s Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that at least 2 minutes will elapse between car arrivals is _____________.
  2. a) 0.0000
  3. b) 0.4493
  4. c) 0.1353
  5. d) 1.0000
  6. e) 1.0225

 

Ans: b

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. On Saturdays, cars arrive at Sam Schmitt’s Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. The probability that less than 10 minutes will elapse between car arrivals is _____________.
  2. a) 0.8465
  3. b) 0.9817
  4. c) 0.0183
  5. d) 0.1535
  6. e) 0.2125

 

Ans: b

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

 

 

  1. Let x be a binomial random variable with n=100 and p=.8. The probability of less than 78 successes, when using the normal approximation for binomial is ________
  2. a) 0.2659
  3. b) 0.5
  4. c) 0.4156
  5. c) 0.0002
  6. d) 0.64
  7. e) 0.04

 

Ans: a

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Hard

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

 

  1. Assuming an equal chance of a new baby being a boy or a girl (that is, p= 0.5), we would like to find the probability of 40 or more of the next 100 births at a local hospital will be boys. Using the normal approximation for binomial with a correction for continuity, we should use the z-score _______
    a) 0.4
  2. b) -2.1
  3. c) 0.6
  4. d) 2
  5. e) -1.7

 

Ans: b

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Hard

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

 

 

  1. The probability that a call to an emergency help line is answered in less than 10 seconds is 0.8. Assume that the calls are independent of each other. Using the normal approximation for binomial with a correction for continuity, the probability that at least 75 of 100 calls are answered within 10 seconds is approximately _______
  2. a) 0.8
  3. b) 0.1313
  4. c) 0.5235
  5. d) 0.9154
  6. e) 0.8687

 

Ans: d

Response: See section 6.3, Using the Normal Curve to Approximate Binomial Distribution Problems

Difficulty: Hard

Learning Objective: 6.3: Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity.

  1. e) 0.95

 

 

 

  1. Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute. The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________
  2. a) 0.05
  3. b) 0.75
  4. c) 0.25
  5. d) 0.27
  6. e) 0.73

 

Ans: a

Response: See section 6.4, Exponential Distribution

Difficulty: Hard

Learning Objective: 6.4: Solve for probabilities in an exponential distribution and contrast the exponential distribution to the discrete Poisson distribution.

 

File: Ch07, Chapter 7: Sampling and Sampling Distributions

 

 

 

True/False

 

 

 

  1. Saving time and money are reasons to take a sample rather than do a census.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

  1. In some situations, sampling may be the only option because the population is inaccessible.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. A population list, map, directory, or other source used to represent the population from which a sample is taken is called the census.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. In a random sampling technique, every unit of the population has a randomly varying chance or probability of being included in the sample.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Cluster (or area) sampling is a type of random sampling technique.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Systematic sampling is a type of nonrandom sampling technique.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. A major limitation of nonrandom samples is that they are not appropriate for most statistical methods.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. The directory or map from which a sample is taken is called the frame.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. The two major categories of sampling methods are proportionate and disproportionate sampling.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. If every unit of the population has the same probability of being selected to the sample, then the researcher is probably conducting random sampling.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. With cluster sampling, there is homogeneity within a subgroup or stratum.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

 

 

 

  1. If a researcher selects every kth item from a population of N items, then she is likely conducting a stratified random sampling.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. If every unit of the population has the same probability of being selected to the sample, then the researcher is conducting random sampling.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. A nonrandom sampling technique that is similar to stratified random sampling is called quota sampling.

 

Ans: True

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Nonsampling error occurs when, due to chance, the sample is not representative of the population.

 

Ans: False

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. A sampling distribution is the distribution of a sample statistic such as the sample mean or sample proportion.

 

Ans: True

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

  1. The standard deviation of a sampling distribution of the sample means is commonly called the standard error of the mean.

 

Ans: True

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. The central limit theorem states that if the sample size, n, is large enough (n ≥30), the distribution of the sample means is uniformly distributed regardless of the shape of the population.

 

Ans: False

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Increasing the sample size causes the numerical value of standard error of the sample means to increase.

 

Ans: False

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. The mean of the sample means is the same as the mean of the population

 

Ans: True

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

  1. If the population is normally distributed, the sample means of size n=5 are normally distributed

 

Ans: True

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. The sampling distribution of the sample means is close to the normal distribution only if the distribution of the population is close to normal.

 

Ans: False

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. The sampling distribution of the sample means is less variable than the population distribution.

 

Ans: True

Response: See section 7.2 Sampling Distribution of x¯

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. The sampling distribution of is close to normal provided that n≥30.

 

Ans: False

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. The sampling distribution of has a mean equal to the population proportion p.

 

Ans: True

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Suppose 90% of students in some specific college have a computer at home and a sample of 40 students is taken. The probability that more than 30 of those in the sample have a computer at home can be approximated using the normal approximation.

 

Ans: False

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

Multiple Choice

 

 

 

  1. Kristen Ashford purchased the subscribers list for Wind Surfing magazine. She plans to survey a sample of the subscribers before using the list in her mail order business.  She chooses the first 100 of the 5,000 names.  Her sample is a _________.
  2. a) simple random sample
  3. b) stratified sample
  4. c) systematic sample
  5. d) convenience sample
  6. e) cluster sample

 

Ans: d

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Kristen Ashford purchased the subscribers list for Wind Surfing magazine. She plans to survey a sample of the subscribers before using the list in her mail order business.  She randomly selects the fourth name as a starting point and then selects every 50th subsequent name (54, 104, 154, etc.).  Her sample is a _________.
  2. a) simple random sample
  3. b) stratified sample
  4. c) systematic sample
  5. d) convenience sample
  6. e) cluster sample

 

Ans: c

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Kristen Ashford purchased the subscribers list for Wind Surfing magazine. She plans to survey a sample of the subscribers before using the list in her mail order business.  The names are numbered consecutively from 1 to 5,000.  Kristen chooses her sample by selecting four-digit numbers (1 to 5,000) from a random number table.  Her sample is a _________.
  2. a) simple random sample
  3. b) stratified sample
  4. c) systematic sample
  5. d) convenience sample
  6. e) cluster sample

 

Ans: a

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. She knows that 2,500 payroll vouchers have been issued since January 1, 2000, and her staff doesn’t have time to inspect each voucher.  So, she orders her staff to inspect the last 200 vouchers.  Her sample is a ___________.
  2. a) stratified sample
  3. b) simple random sample
  4. c) convenience sample
  5. d) systematic sample
  6. e) cluster sample

 

Ans: c

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. She knows that 2,500 payroll vouchers have been issued since January 1, 2000, and her staff doesn’t have time to inspect each voucher.  So, she randomly selects 53 as a starting point and orders her staff to inspect the 53rd voucher and each voucher at an increment of 100 (53, 153, 253, etc.).  Her sample is a ___________.
  2. a) stratified sample
  3. b) simple random sample
  4. c) convenience sample
  5. d) cluster sample
  6. e) systematic sample

 

Ans: e

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Financial analyst Larry Potts needs a sample of 100 securities listed on the New York Stock Exchange. In the current issue of the Wall Street Journal, 2,531 securities are listed in the “New York Exchange Composite Transactions,” an alphabetical listing of all securities traded on the previous business day.  Larry uses a table of random numbers to select 100 numbers between 1 and 2,531.  His sample is a ____________.
  2. a) quota sample
  3. b) simple random sample
  4. c) systematic sample
  5. d) stratified sample
  6. e) cluster sample

 

Ans: b

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Financial analyst Larry Potts needs a sample of 100 securities listed on the New York Stock Exchange. In the current issue of the Wall Street Journal, 2,531 securities are listed in the “New York Exchange Composite Transactions,” an alphabetical listing of all securities traded on the previous business day.  Larry randomly selects the 7th security as a starting point, and selects every 25th security thereafter (7, 32, 57, etc.).  His sample is a ____________.
  2. a) quota sample
  3. b) simple random sample
  4. c) stratified sample
  5. d) systematic sample
  6. e) cluster sample

 

Ans: d

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Financial analyst Larry Potts needs a sample of 100 securities listed on either the New York Stock Exchange (NYSE) or the American Stock Exchange (AMEX). According to the Wall Street Journal’s “Stock Market Data Bank,” 2,531 NYSE securities and AMEX 746 securities were traded on the previous business day.  Larry directs his staff to randomly select 77 NYSE and 23 AMEX securities.  His sample is a ____________.
  2. a) disproportionate systematic sample
  3. b) disproportionate stratified sample
  4. c) proportionate stratified sample
  5. d) proportionate systematic sample
  6. e) proportionate cluster sampling

 

Ans: c

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. On Saturdays, cars arrive at David Zebda’s Scrub and Shine Car Wash at the rate of 80 cars per hour during the ten-hour shift. David wants a sample of 40 Saturday customers to answer the long version of his quality service questionnaire.  He instructs the Saturday crew to select the first 40 customers.  His sample is a __________.
  2. a) convenience sample
  3. b) simple random sample
  4. c) systematic sample
  5. d) stratified sample
  6. e) cluster sample

 

Ans: a

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. On Saturdays, cars arrive at David Zebda’s Scrub and Shine Car Wash at the rate of 80 cars per hour during the ten-hour shift. David wants a sample of 40 Saturday customers to answer the long version of his quality service questionnaire.  He randomly selects 9 as a starting point and instructs the crew to select the 9th customer and each customer at intervals of 20 (9, 29, 49, etc.).  His sample is a __________.
  2. a) convenience sample
  3. b) simple random sample
  4. c) unsystematic sample
  5. d) stratified sample
  6. e) systematic sample

 

Ans: e

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers.  Albert instructs his staff to record the waiting times for the first 45 walk-in customers arriving after the noon hour.  Albert’s sample is a ________.
  2. a) simple random sample
  3. b) systematic sample
  4. c) convenience sample
  5. d) stratified sample
  6. e) cluster sample

 

Ans: c

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers.  Albert randomly selects 4 as a starting point and instructs his staff to record the waiting times for the 4th walk-in customer and every 10th customer thereafter (4, 14, 24, etc.).  Albert’s sample is a ________.
  2. a) simple random sample
  3. b) cluster sample
  4. c) convenience sample
  5. d) stratified sample
  6. e) systematic sample

 

Ans: e

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. A carload of palletized aluminum castings has arrived at Mansfield Motor Manufacturers. The car contains 1,000 pallets of 100 castings each.  Mario Munoz, manager of Quality Assurance, directs the receiving crew to deliver the 127th and 869th pallets to his crew for 100% inspection.  Mario randomly selected 127 and 869 from a table of random numbers.  Mario’s sample of 200 castings is a _____________.
  2. a) simple random sample
  3. b) systematic sample
  4. c) stratified sample
  5. d) cluster sample
  6. e) convenience sample

 

Ans: d

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 1,000 bundles of 50 rods each.  Claude Ong, manager of Quality Assurance, directs the receiving crew to deliver the 63rd and 458th bundles to his crew for 100% inspection.  Claude randomly selected 63 and 458 from a table of random numbers.  Claude’s sample of 100 rods is a _____________.
  2. a) cluster sample
  3. b) simple random sample
  4. c) quota sample
  5. d) systematic sample
  6. e) stratified sample

 

Ans: a

Response: See section 7.1 Sampling

Difficulty: Medium

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments.  For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers.  He orders a random sample of 10 workers from each of the six departments.  Abel’s sample is a ________________.
  2. a) proportionate systematic sample
  3. b) proportionate stratified sample
  4. c) disproportionate systematic sample
  5. d) disproportionate stratified sample
  6. e) proportionate cluster sample

 

Ans: d

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments.  For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers.  He orders a random sample of 10% of the workers from each of the six departments.  Abel’s sample is a ________________.
  2. a) proportionate systematic sample
  3. b) proportionate stratified sample
  4. c) disproportionate systematic sample
  5. d) disproportionate stratified sample
  6. e) proportionate cluster sample

 

Ans: b

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. Catherine Chao, Director of Marketing Research, needs a sample of households to participate in the testing of a new toothpaste package. She chooses thirty-six of her closest friends.  Catherine’s sample is a _____________.
  2. a) cluster sample
  3. b) convenience sample
  4. c) quota sample
  5. d) systematic sample
  6. e) random sample

 

Ans: b

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

 

  1. Catherine Chao, Director of Marketing Research, needs a sample of households to participate in the testing of a new toothpaste package. She directs the seven members of her staff to find five households each.  Catherine’s sample is a _____________.
  2. a) cluster sample
  3. b) proportionate stratified sample
  4. c) quota sample
  5. d) disproportionate stratified sample
  6. e) simple random sample

 

Ans: c

Response: See section 7.1 Sampling

Difficulty: Easy

Learning Objective: 7.1: Contrast sampling to census and differentiate among different methods of sampling, which include simple, stratified, systematic, and cluster random sampling; and convenience, judgment, quota, and snowball nonrandom sampling, by assessing the advantages associated with each.

 

 

 

  1. According to the central limit theorem, if a sample of size 100 is drawn from a population with a mean of 80, the mean of all sample means would equal _______.
  2. a) 80
  3. b) 8
  4. c) 80
  5. d) 100
  6. e) 120

 

Ans: c

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, if a sample of size 64 is drawn from a population with a mean of 56, the mean of all sample means would equal _______.
  2. a) 00
  3. b) 56.00
  4. c) 64.00
  5. d) 0.875
  6. e) 128.00

 

Ans: b

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, if a sample of size 81 is drawn from a population with a standard deviation of 72, the standard deviation of the distribution of the sample means would equal _______.
  2. a) 8
  3. b) 9
  4. c) 7.2
  5. d) 0.875
  6. e) 128.00

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, if a sample of size 100 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal _______.
  2. a) 80
  3. b) 8
  4. c) 80
  5. d) 800
  6. e) 0.080

 

Ans: b

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, if a sample of size 64 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal _______.
  2. a) 000
  3. b) 1.250
  4. c) 0.125
  5. d) 0.800
  6. e) 0.080

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Increasing the sample size causes the sampling distribution of to ________.
  2. a) shift to the right
  3. b) shift to the left
  4. c) have more dispersion
  5. d) have less dispersion
  6. e) stay unchanged

 

Ans: d

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, for samples of size 64 drawn from a population with m = 800 and s = 56, the mean of the sampling distribution of sample means would equal _______.
  2. a) 7
  3. b) 8
  4. c) 100
  5. d) 800
  6. e) 80

 

Ans: d

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, for samples of size 64 drawn from a population with m = 800 and s = 56, the standard deviation of the sampling distribution of sample means would equal _______.
  2. a) 7
  3. b) 8
  4. c) 100
  5. d) 800
  6. e) 80

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, for samples of size 169 drawn from a population with m = 1,014 and s = 65, the mean of the sampling distribution of sample means would equal _______.
  2. a) 1,014
  3. b) 65
  4. c) 5
  5. d) 6
  6. e) 3

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. According to the central limit theorem, for samples of size 169 drawn from a population with m = 1,014 and s = 65, the standard deviation of the sampling distribution of sample means would equal _______.
  2. a) 1,014
  3. b) 65
  4. c) 15
  5. d) 6
  6. e) 5

 

Ans: e

Response: See section 7.2 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of more than 95 is _______.
  2. a) 0.1056
  3. b) 0.3944
  4. c) 0.4286
  5. d) 0.8944
  6. e) 1.0000

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of less than 84 is _______.
  2. a) 0.9332
  3. b) 0.0668
  4. c) 0.4332
  5. d) 0.8664
  6. e) 1.0000

 

Ans: b

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean between 85 and 95 is _______.
  2. a) 0.1056
  3. b) 0.3944
  4. c) 0.7888
  5. d) 0.2112
  6. e) 0.5000

 

Ans: c

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean between 80 and 100 is _______.
  2. a) 0.9876
  3. b) 0.0124
  4. c) 0.4938
  5. d) 0.0062
  6. e) 1.0000

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean of more than 404.5 is _______.
  2. a) 0.0139
  3. b) 0.4861
  4. c) 0.4878
  5. d) 0.0122
  6. e) 0.5000

 

Ans: d

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean between 395.5 and 404.5 is _______.
  2. a) 0.9756
  3. b) 0.0244
  4. c) 0.0278
  5. d) 0.9722
  6. e) 1.0000

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean less than 402 is _______.
  2. a) 0.3413
  3. b) 0.6826
  4. c) 0.8413
  5. d) 0.1587
  6. e) 0.9875

 

Ans: c

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 450 and a variance of 900. If a random sample of size 100 is drawn from the population, the probability that the sample mean is between 448 and 453 is _______.
  2. a) 0.4972
  3. b) 0.6826
  4. c) 0.4101
  5. d) 0.5899
  6. e) 0.9878

 

Ans: d

Response: See section 7.2 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 870 and a variance of 1,600. If a random sample of size 64 is drawn from the population, the probability that the sample mean is between 860 and 875 is _______.
  2. a) 0.9544
  3. b) 0.6826
  4. c) 0.8785
  5. d) 0.5899
  6. e) 0.8185

 

Ans: e

Response: See section 7.2 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose a population has a mean of 870 and a variance of 8,100. If a random sample of size 36 is drawn from the population, the probability that the sample mean is between 840 and 900 is _______.
  2. a) 0.9544
  3. b) 0.6826
  4. c) 0.8185
  5. d) 0.5899
  6. e) 0.0897

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers.  If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert’s sample of 64 will have a mean less than 14 minutes is ________.
  2. a) 0.4772
  3. b) 0.0228
  4. c) 0.9772
  5. d) 0.9544
  6. e) 1.0000

 

Ans: b

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers.  If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert’s sample of 64 will have a mean less than 16 minutes is ________.
  2. a) 0.4772
  3. b) 0.0228
  4. c) 0.9072
  5. d) 0.9544
  6. e) 0.9772

 

Ans: e

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers.  If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert’s sample of 64 will have a mean less than 15 minutes is ________.
  2. a) 0.5000
  3. b) 0.0228
  4. c) 0.9072
  5. d) 0.9544
  6. e) 1.0000

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers.  If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert’s sample of 64 will have a mean between 13.5 and 16.5 minutes is ________.
  2. a) 0.9974
  3. b) 0.4987
  4. c) 0.9772
  5. d) 0.4772
  6. e) 0.5000

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods.  Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods.  If the population of rods has a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude’s sample has a mean greater than 120.0125 inches is _____________.
  2. a) 0.0124
  3. b) 0.0062
  4. c) 0.4938
  5. d) 0.9752
  6. e) 1.0000

 

Ans: b

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods.  Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods.  If the population of rods have a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude’s sample has a mean less than 119.985 inches is _____________.
  2. a) 0.9974
  3. b) 0.0026
  4. c) 0.4987
  5. d) 0.0013
  6. e) 0.0030

 

Ans: d

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods.  Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods.  If the population of rods has a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude’s sample has a mean between 119.985 and 120.0125 inches is ____________.
  2. a) 0.9925
  3. b) 0.9974
  4. c) 0.9876
  5. d) 0.9544
  6. e) 0.9044

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. Suppose 40% of the population possess a given characteristic. If a random sample of size 300 is drawn from the population, then the probability that 44% or fewer of the samples possess the characteristic is _______.
  2. a) 0.0793
  3. b) 0.4207
  4. c) 0.9207
  5. d) 0.9900
  6. e) 1.0000

 

Ans: c

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

  1. Suppose 30% of a population possess a given characteristic. If a random sample of size 1200 is drawn from the population, then the probability that less than 348 possess that characteristic is _______.
  2. a) 0.2236
  3. b) 0.2764
  4. c) 0.2900
  5. d) 0.7764
  6. e) 0.3336

 

Ans: a

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is less than 0.88?
  2. a) 0.2019
  3. b) 0.2981
  4. c) 0.5300
  5. d) 0.7019
  6. e) 0.7899

 

Ans: b

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89?
  2. a) 0.1064
  3. b) 0.2700
  4. c) 0.3936
  5. d) 0.6064
  6. e) 0.9000

 

Ans: d

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Suppose 40% of all college students have a computer at home and a sample of 64 is taken. What is the probability that more than 30 of those in the sample have a computer at home?
  2. a) 0.3686
  3. b) 0.1314
  4. c) 0.8686
  5. d) 0.6314
  6. e) 0.1343

 

Ans: b

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Suppose 40% of all college students have a computer at home and a sample of 100 is taken. What is the probability that more than 50 of those in the sample have a computer at home?
  2. a) 0.4793
  3. b) 0.9793
  4. c) 0.0207
  5. d) 0.5207
  6. e) 0.6754

 

Ans: c

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. If 10% of the 5,000 payroll vouchers issued since January 1, 2000, have irregularities, the probability that Pinky’s random sample of 200 vouchers will have a sample proportion greater than .06 is ___________.
  2. a) 0.4706
  3. b) 0.9706
  4. c) 0.0588
  5. d) 0.9412
  6. e) 0.9876

 

Ans: b

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. If 10% of the 5,000 payroll vouchers issued since January 1, 2000, have irregularities, the probability that Pinky’s random sample of 200 vouchers will have a sample proportion of between .06 and .14 is ___________.
  2. a) 4706
  3. b) 0.9706
  4. c) 0.0588
  5. d) 0.9412
  6. e) 0.8765

 

Ans: d

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City prefer the new package, the probability that Catherine’s random sample of 300 households will have a sample proportion greater than 0.45 is ___________.
  2. a) 0.9232
  3. b) 0.0768
  4. c) 0.4616
  5. d) 0.0384
  6. e) 0.8974

 

Ans: d

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package. If 40% of the households in Kansas City prefer the new package, the probability that Catherine’s random sample of 300 households will have a sample proportion between 0.35 and 0.45 is ___________.
  2. a) 0.9232
  3. b) 0.0768
  4. c) 0.4616
  5. d) 0.0384
  6. e) 0.8976

 

Ans: a

Response: See section 7.3 Sampling Distribution of

Difficulty: Hard

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. A random sample of size 100 is drawn from a population with a standard deviation of 10. If only 5% of the time a sample mean greater than 20 is obtained, the mean of the population is ______
  2. a) 18.35
  3. b) 16.25
  4. c) 17.2
  5. d) 20
  6. e) 19

 

Ans: a

Response: See section 7.2 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.2: Describe the distribution of a sample’s mean using the central limit theorem, correcting for a finite population if necessary.

 

 

 

  1. In an instant lottery, your chance of winning is 0.1. If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is
  2. a) 0.4933
  3. b) 0.5
  4. c) .15
  5. d) 0.0478
  6. e) 0.9213

 

Ans: d

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Suppose 40% of all college students have a computer at home and a sample of 100 students is taken. The mean of the sampling distribution of is
  2. a) 0.4
  3. b) 0.04
  4. c) 40
  5. d) 0.004
  6. e) 4

 

Ans: a

Response: See section 7.3 Sampling Distribution of

Difficulty: Easy

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.

 

 

 

  1. Suppose 40% of all college students have a computer at home and a sample of 100 is taken. The standard deviation of the sampling distribution of is
  2. a) 89
  3. b) 0.0489
  4. c) 0.24
  5. d) 24
  6. e) 0.4

 

Ans: b

Response: See section 7.3 Sampling Distribution of

Difficulty: Medium

Learning Objective: 7.3: Describe the distribution of a sample’s proportion using the z formula for sample proportions.