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

Description

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 50^th 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 75^th 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 90^th 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 k^th 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.