Business Statistics In Practice 8th Edition By Bowerman – Test Bank

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Sample Questions Posted Below

 

 

 

 

Chapter 05 Test Bank – Static KEY

 

1. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and is such that the probability of success on any trial is the same.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
2. A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space.

FALSE

Poisson random variables are not continuous, they are discrete.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

3. A discrete random variable may assume a countable number of outcome values.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable.
Topic: Two Types of Random Variables
4. The variable Home Ownership can take on one of two values, 1 if the person living in a home owns the home and 0 if the person living in a home does not own the home. This is an example of a discrete random variable.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable.
Topic: Two Types of Random Variables

 

 

 

 

 

 

 

 

 

 

 

5. If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

FALSE

This example is a description of a hypergeometric distribution.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
6. The mean of the binomial distribution is np(1 − p).

FALSE

The mean of the binomial is np.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

7. In a binomial experiment, the results of one trial are dependent on the results of other trials.

FALSE

One assumption of the binomial distribution is independence of trials.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
8. In a binomial distribution, the random variable X is continuous.

FALSE

The binomial distribution defines the random variable as discrete.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

9. The internal auditor for your company believes that 10 percent of their invoices contain errors. To check this theory, 20 invoices are randomly selected and 5 are found to have errors.
The claim of the auditor will be rejected.

TRUE

Reject claim because P < .05.

AACSB: Analytical Thinking
Blooms: Analyze
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
10. The mean and the variance of a Poisson random variable are equal.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

11. Depending on the mean of the Poisson distribution, the distribution can either be very skewed to the right or quite symmetrical.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
12. For a discrete probability distribution, the value of p(x) for each value of x falls between −1 and 1.

FALSE

Probability values can only fall between 0 and 1.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

13. The expected value of the discrete random variable x is the population mean.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

14. The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

15. The time (in seconds) it takes for an athlete to run 50 meters is an example of a continuous random variable.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable.
Topic: Two Types of Random Variables
16. The hypergeometric probability distribution can be approximated by the Poisson distribution.

FALSE

The hypergeometric distribution is approximated by a binomial distribution.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

17. If the population size is at least 20 times larger than the sample size, a hypergeometric distribution can be approximated by the binomial distribution.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution
18. In a hypergeometric probability distribution of a population of N items, r refers to the number of successes and Nr to the number of failures.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

 

 

 

19. With two random variables x and y, a positive covariance says that as x increases, y tends to increase in a linear fashion.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-06 Compute and understand the covariance between two random variables.
Topic: Joint Distributions and the Covariance
20. A correlation coefficient is a unitless measure of the linear relationship between two random variables.

TRUE

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-06 Compute and understand the covariance between two random variables.
Topic: Joint Distributions and the Covariance

 

21. The property of expected values says if a and b are constants, and if x and y are random variables, then μ(ax +by) = x + y + 2ab.

FALSE

The property of expected values does not include the value 2ab.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-06 Compute and understand the covariance between two random variables.
Topic: Joint Distributions and the Covariance
22. The random variable x has a hypergeometric distribution, and the population contains 12 items. If you wanted to find the number of defects in a random sample of 3 selected items when the population contains 5 defects, identify the N, n, and r.

 

A. N = 3, n = 12, r = 5

 

B. N = 5, n = 12, r = 7

 

C. N = 12, n = 5, r = 3

 

D. N = 12, n = 3, r = 5

In the hypergeometric distribution, N is the number of items in the population, r the number of successes, and n a random sample of the population N.

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

 

 

 

 

 

 

23. A hypergeometric random variable x has a distribution that is approximated by a binomial distribution when

 

A. the number of successes is larger than the number of failures in the population.

 

B. a sample is selected from the population without replacement.

 

C. the population is much larger than the sample size.

 

D. the sample size is half the size of the original population.

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution
24. In the context of the hypergeometric distribution, r is

 

A. sample size.

 

B. the number of items in the population that are successes.

 

C. the number of items that are sampled without replacement.

 

D. the number of items in the sample that are successes.

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

25. Which of the following is not a discrete random variable?

 

A. the number of times a light changes red in a 10-minute cycle

 

B. the number of minutes required to run 1 mile

 

C. the number of defects in a sample selected from a population of 100 products

 

D. the number of criminals found in a five-mile radius of a neighborhood

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 1 Easy
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable.
Topic: Two Types of Random Variables

 

26. A random variable

 

A. is the result of a measurement.

 

B. can only be discrete.

 

C. assigns one and only one numeric value to each experimental outcome.

 

D. is a binomial, Poisson, or hypergeometric variable.

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable.
Topic: Two Types of Random Variables

 

 

27. A discrete probability distribution is expressed as a table, graph, or ___________ that gives the probability associated with each possible value that the random variable can assume.

 

A. binomial

 

B. formula

 

C. Poisson

 

D. hypergeometric

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
28. Using the following probability distribution table of the random variable x, what is the probability of x = 3?
 

 

A. 3/15

 

B. 5/15

 

C. 1/15

 

D. 2/15

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 1 Easy
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

29. The probability distribution of a random variable that is defined to be the number of successes obtained in a random sample selected without replacement from a finite population of N elements that contains r successes and Nr failures is

 

A. Poisson.

 

B. binomial.

 

C. hypergeometric.

 

D. discrete.

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

30. The mean of a hypergeometric random variable is defined as

 

A. n × (r/N).

 

B. N × (r/n).

 

C. npq.

 

D. np.

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

 

31. If p = .1 and n = 5, then the corresponding binomial distribution is ____________.

 

A. right skewed

 

B. left skewed

 

C. symmetric

 

D. bimodal

 

AACSB: Reflective Thinking
Blooms: Analyze
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
32. If p = .5 and n = 4, then the corresponding binomial distribution is ____________.

 

A. right skewed

 

B. left skewed

 

C. symmetric

 

D. bimodal

 

AACSB: Reflective Thinking
Blooms: Analyze
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

33. The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.

 

A. binomial

 

B. uniform

 

C. normal

 

D. Poisson

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
34. If the number of surface nonconformities on a specific size of metal piece is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defects is given most likely by _________________ distribution(s).

 

A. the binomial

 

B. the Poisson

 

C. the hypergeometric

 

D. both the binomial and Poisson

 

AACSB: Reflective Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

35. Which of the following distributions can be used to solve the following problem?
The average number of cars arriving at a drive-through fast-food restaurant is three in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

 

A. binomial

 

B. Poisson

 

C. both binomial and Poisson

 

D. neither binomial nor Poisson

 

AACSB: Reflective Thinking
Blooms: Analyze
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

 

 

36. The mean of the binomial distribution is equal to

 

A. p.

 

B. np.

 

C. px(1 − p)nx.

 

D. (n)(p)(1 − p).

 

E.  

 

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

37. The number of ways to arrange x successes among n trials is equal to

 

A. .

 

B. .

 

C. .

 

D. .

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

38. Which of the following is a valid probability value for a discrete random variable?

 

A. .2

 

B. 1.01

 

C. −.7

 

D. All of the choices are correct.

The probability of a discrete random variable can only be between 0 and +1.

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

 

 

 

 

 

 

 

 

 

 

 

39. A total of 50 raffle tickets are sold for a contest to win a car. If you purchase one ticket, what are your odds against winning?

 

A. 49 to 1

 

B. 50 to 1

 

C. .05

 

D. .01

Probability of losing = 1 − probability of winning = 1 − 1/50 = 49/50.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
40. Which one of the following statements is not an assumption of the binomial distribution?

 

A. Sampling is with replacement.

 

B. The experiment consists of n identical trials.

 

C. The probability of success remains constant from trial to trial.

 

D. Trials are independent of each other.

 

E. Each trial results in one of two mutually exclusive outcomes.

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

41. The binomial distribution is characterized by situations that are analogous to

 

A. drawing balls from an urn.

 

B. coin tossing.

 

C. counting defects on an item.

 

D. measuring the length of an item.

Binomial distributions assume a constant probability of success.

AACSB: Reflective Thinking
Blooms: Evaluate
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
42. Two characteristics, or assumptions, of the Poisson distribution are that

 

A. the probability of success remains constant from trial to trial, and the random variable of interest is continuous.

 

B. the event occurring in one interval is independent of the event occurring in any other nonoverlapping interval, and the random variable of interest is continuous.

 

C. the event occurring in one interval is independent of the event occurring in any other nonoverlapping interval, and the random variable of interest is discrete.

 

D. the event occurring in one interval is dependent on the event occurring in any other nonoverlapping interval, and the random variable of interest is continuous.

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

43. The variable Employment Status, which can take either the value 1 for Employed and 0 for Unemployed, is an example of a _____________ random variable.

 

A. Poisson

 

B. discrete

 

C. hypergeometric

 

D. continuous

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable.
Topic: Two Types of Random Variables
44. If x is a binomial random variable, then the standard deviation of x is given by

 

A. np.

 

B. (npq)2.

 

C. npq.

 

D. npq.

 

AACSB: Analytical Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

45. A random variable that is defined to be the total number of successes in n trials is a __________ random variable.

 

A. binomial

 

B. Poisson

 

C. hypergeometric

 

D. continuous

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

46. A discrete variable that can often be used to describe the number of occurrences of an event over a specified interval of time or space is a ___________ random variable.

 

A. Poisson

 

B. discrete

 

C. hypergeometric

 

D. continuous

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

47. The requirement that the probability of success remains constant from trial to trial is a property of the _______________ distribution.

 

A. binomial

 

B. Poisson

 

C. hypergeometric

 

D. continuous

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

48. The distribution whose mean is equal to its variance is the _________ distribution.

 

A. binomial

 

B. Poisson

 

C. hypergeometric

 

D. continuous

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

49. For a random variable X, the mean value of the squared deviations of its values from their expected value is called its ____________.

 

A. standard deviation

 

B. mean

 

C. probability

 

D. variance

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Two Types of Random Variables
50. When p = .5, the binomial distribution will _________ be symmetric.

 

A. always

 

B. sometimes

 

C. never

 

AACSB: Analytical Thinking
Blooms: Understand
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

51. Which of the following statements about the binomial distribution is not correct?

 

A. Each trial results in a success or failure.

 

B. Trials are independent of each other.

 

C. The probability of success remains constant from trial to trial.

 

D. The random variable of interest is continuous.

 

E. The experiment consists of n identical trials.

 

AACSB: Reflective Thinking
Blooms: Remember
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

52. If n = 15 and p = .4, then the standard deviation of the binomial distribution is

 

A. 9.

 

B. 6.

 

C. 3.6.

 

D. 1.897.

 

E. .4.

Standard deviation = √npq = √[(15)(.4)(.6)] = √3.6 = 1.897

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

53. The equation for the variance of the binomial distribution is given by

 

A. px(1 − p)nx.

 

B. np.

 

C. np(1 − p).

 

D.

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
54. The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that exactly 4 bankruptcies occur next month.

 

A. .8774

 

B. .1414

 

C. .1557

 

D. .2176

P(4) = e−2.6(2.6)4/4! (e = 2.71828)

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

55. The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that more than 1 bankruptcy occurs next month.

 

A. .1931

 

B. .9257

 

C. .7326

 

D. .4816

 

E. .2674

P(1) = e−2.6(2.6)1/1! (e = 2.71828)

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
56. The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that no more than one bankruptcy occurs next month.

 

A. .1931

 

B. .9257

 

C. .7326

 

D. .4816

 

E. .2674

P(X = 0 or X = 1) = e−2.6(2.6)0/0! + e−2.6(2.6)1/1! (e = 2.71828)

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

57. A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur fewer than 3 times?

 

A. .0547

 

B. .1172

 

C. .1550

 

D. .7752

 

E. .8450

Σ P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 1, 3, 5; or look up in binomial table where x = 1 or 3 or 5 when p = .3 and n = 10.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

58. A fair die is rolled 10 times. What is the probability that an even number (2, 4, or 6) will occur between 2 and 4 times?

 

A. .6123

 

B. .1709

 

C. .1611

 

D. .3662

 

E. .3223

Σ P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 2, 4, 6; or look up in binomial table, where x = 2 or 4 or 6 when p = .3 and n = 10.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

59. A fair die is rolled 10 times. What is the average number of even number outcomes?

 

A. 3

 

B. 4

 

C. 5

 

D. 6

 

E. 7

Binomial mean = μ = np = 10(.5) = 5

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
60. A fair die is rolled 36 times. What is the standard deviation of the even number (2, 4, or 6) outcomes?

 

A. 18

 

B. 9

 

C. 5

 

D. 3

 

E. 1.732

Binomial standard deviation = σ = √(npg) = √[(36)(.5)(.5)] = √9 = 3

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

61. The manager of the local grocery store has determined that, on average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period, exactly 2 customers use the service desk?

 

A. .0183

 

B. .0733

 

C. .1465

 

D. .9084

 

E. .7619

P(2) = e−4(4)2/2! (e = 2.71828)

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

 

 

62. The manager of the local grocery store has determined that, on average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period, no more than 2 customers use the service desk?

 

A. .2381

 

B. .1465

 

C. .7619

 

D. .8535

 

E. .0916

P(x < 3) = Σ e−μ(μ)x/x!, for x = 0, 1, 2 (e = 2.71828)

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

63. The probability that a given computer chip will fail is 0.02. Find the probability that of 5 delivered chips, exactly 2 will fail.

 

A. .9039

 

B. .0922

 

C. .0038

 

D. .0000

P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 2, n = 5, p = 0.02

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
64. According to a survey of adults, 64 percent have money in a bank savings account. If we were to survey 50 randomly selected adults, find the mean number of adults who would have bank savings accounts.

 

A. 12

 

B. 22

 

C. 32

 

D. 42

Mean = np = 50(.64) = 32

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

 

 

 

 

 

 

 

 

 

 

65. In the most recent election, 19 percent of all eligible college students voted. If a random sample of 20 students were surveyed, find the probability that exactly half voted in the election.

 

A. .0000

 

B. .0014

 

C. .0148

 

D. .4997

P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 10, when p = .19 and n = 20.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
66. In the most recent election, 19 percent of all eligible college students voted. If a random sample of 20 students were surveyed, find the probability that none of the students voted.

 

A. .0000

 

B. .0014

 

C. .0148

 

D. .4997

P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 0 when p = .19 and n = 20.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

67. Of all individual tax returns, 37 percent include errors made by the taxpayer. If IRS examiners are assigned randomly selected returns in batches of 12, find the mean and standard deviation for the number of erroneous returns per batch.

 

A. μ = 2.80, σ = 1.67

 

B. μ = 4.44, σ = 1.67

 

C. μ = 4.44, σ = 2.80

 

D. μ = 7.56, σ = 2.80

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

68. In a study conducted for the state Department of Education, 30 percent of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.

 

A. .3000

 

B. .2668

 

C. .2001

 

D. .0090

P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 4, when p = .3 and n = 10

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

69. An appliance manufacturer gives a warranty, and 95 percent of its appliances do not require repair before the warranty expires. An organization buys 10 of these appliances. Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

 

A. [8.12, 10.88]

 

B. [7.43, 11.57]

 

C. [8.81, 10.19]

 

D. [8.55, 10.45]

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
70. A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good. If additional tests are to be conducted with random samples of 160 semiconductor chips, find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number).

 

A. 56

 

B. 35

 

C. 29

 

D. 25

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

71. A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that fewer than 4 support increased spending on environmental issues.

 

A. .0330

 

B. .7844

 

C. .9624

 

D. .9954

Σ P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 0, 1, 2, 3 when p = .25 and n = 6.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
72. A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that exactly 3 support increased spending on environmental issues.

 

A. .0330

 

B. .1318

 

C. .7844

 

D. .9624

P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 3 when p = .25 and n = 6.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

73. A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that only 1 supports increased spending on environmental issues.

 

A. .0330

 

B. .1318

 

C. .3560

 

D. .7844

P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 1 when p = .25 and n = 6.

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

 

 

 

 

74. A multiple-choice test has 30 questions and each one has five possible answers, of which only one is correct. If all answers were guesses, find the probability of getting exactly four correct answers.

 

A. .0604

 

B. .1325

 

C. .2552

 

D. .8000

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: The Binomial Distribution

 

 

75. The J.O. Supplies Company buys calculators from a non-US supplier. The probability of a defective calculator is 10 percent. If 3 calculators are selected at random, what is the probability that one of the calculators will be defective?

 

 

A. .0702

 

B. .0010

 

C. .2430

 

D. .7290

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

76. The J.O. Supplies Company buys calculators from a non-US supplier. The probability of a defective calculator is 10 percent. If 10 calculators are selected at random, what is the probability that 3 or more of the calculators will be defective?

 

A. .0702

 

B. .2639

 

C. .0016

 

D. 0

P(X ≥ 3) = 1 − P(X ≤ 2) = 1 − .9298 = .0702

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

77. The J.O. Supplies Company buys calculators from a non-US supplier. The probability of a defective calculator is 10 percent. If 100 calculators are selected at random, what is the expected number of defectives?

 

A. 9

 

B. 90

 

C. 10

 

D. 95

E[X] = μx = (.10)(100) = 10

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
78. The J.O. Supplies Company buys calculators from a non-US supplier. The probability of a defective calculator is 10 percent. If 100 calculators are selected at random, what is the standard deviation of the number of defectives?

 

A. 9.00

 

B. 3.17

 

C. 9.49

 

D. 3.00

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

79. Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours. Assume that the patient arrivals are distributed according to a Poisson distribution. Determine the probability of 6 patients arriving in a five-hour period.

 

A. .136

 

B. .109

 

C. .246

 

D. .001

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
80. Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to a Poisson distribution. Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.

 

A. .3813

 

B. .5711

 

C. .4276

 

D. .7861

 

E. .6174

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

81. The probability distribution of X is

What is the expected value of X?

 

 

A. 1.0

 

B. 5.0

 

C. 2.25

 

D. 2.24

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
82. The probability distribution of X is

What is the variance of X?

 

 

A. 2.25

 

B. 1.0

 

C. 2.24

 

D. 5.0

 

E. 2.25

 

F. 2.24

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

 

 

 

 

 

 

 

 

 

 

 

83. Assume the number of trucks passing an intersection has a Poisson distribution with a mean of 5 trucks per minute. What is the probability of 0 or 1 trucks in one minute?

 

A. .0404

 

B. .0337

 

C. .0842

 

D. .0067

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
84. A vaccine is 95 percent effective. What is the probability that it is not effective for 1 and only 1 individual out of 20 individuals?

 

A. .0179

 

B. .3585

 

C. .0189

 

D. .3774

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

85. A vaccine is 95 percent effective. What is the probability that it is not effective for more than 1 out of 20 individuals?

 

A. .7359

 

B. .3585

 

C. .2641

 

D. .3774

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
86. If the probability of a success on a single trial is .2, what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

 

A. .0031

 

B. .5033

 

C. .1074

 

D. .2013

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

87. The number of calls coming into a call center follows a Poisson process with a mean of 120 calls per hour. What is the probability of no calls in a one-minute interval?

 

A. 0

 

B. .1353

 

C. .4060

 

D. .3679

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
88. If x is a Poisson random variable with a mean of 10, what is the probability that x is greater than 6?

 

A. .9329

 

B. .7797

 

C. .8698

 

D. .0002

P(X ≥ 7) = 1 − P(X ≤ 6) = 1 − (.1302) = .8698

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

89. Three candidates run for different offices in different cities. Each has a one in three chance of being elected in his/her city. What is the probability that at least one of them will be elected?

 

A. .2963

 

B. .7037

 

C. .33

 

D. .667

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
90. A test has 6 multiple choice questions, each with 4 alternatives. What is the probability of guessing 5 or more questions correctly?

 

A. .5340

 

B. .4660

 

C. .9954

 

D. .0046

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

91. If x is a Poisson random variable with a mean of 10, what is the probability that x is greater than or equal to 2?

 

A. .9972

 

B. .0028

 

C. .9995

 

D. .0005

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

 

92. If x is a Poisson random variable with a mean of 10, what is the probability that x is equal to 8?

 

 

A. .1126

 

B. .1251

 

C. .2677

 

D. .0993

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

93. Twenty coins are tossed. What is the probability of getting exactly 10 heads?

 

A. .3364

 

B. .1602

 

C. .5000

 

D. .1762

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
94. Determine the probability that a 3 will appear twice, if a single fair die is rolled 10 times.

 

A. .5010

 

B. .2907

 

C. .2318

 

D. .0065

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

95. During off hours, cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute. The arrivals are distributed according to a Poisson distribution. What is the probability that during the next minute, three cars will arrive?

 

A. .0758

 

B. .1255

 

C. .0126

 

D. .0613

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
96. During off hours, cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute. The arrivals are distributed according to a Poisson distribution. What is the probability that during the next five minutes, three cars will arrive?

 

A. .2138

 

B. .1804

 

C. .0126

 

D. .0613

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
97. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the expected value.

 

A. 5.0

 

B. 1.2

 

C. 2.0

 

D. 1.1

E[X] = (5)(.40) = 2

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
98. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the variance.

 

A. 5.0

 

B. 1.2

 

C. 2.0

 

D. 1.1

σ2x = (5)(.4)(.6) = 1.2

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

99. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the standard deviation.

 

A. 5.0

 

B. 1.2

 

C. 2.0

 

D. 1.1

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
100. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X £ 1).

 

A. .0870

 

B. .2592

 

C. .0778

 

D. .3370

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

101. For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X > 4).

 

A. .0102

 

B. .0778

 

C. .0870

 

D. .3370

P(X = 5) = (.4)5 = .0102

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
102. Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. Determine the expected number of customer arrivals for a five-minute period.

 

A. 15

 

B. 3

 

C. 243

 

D. 125

μ = (3)(5) = 15

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

103. Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the expected value of X.

 

A. 3

 

B. 9

 

C. 1.5

 

D. 1.7

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
104. Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the variance of X.

 

A. 3

 

B. 9

 

C. 1.5

 

D. 1.7

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

105. Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the standard deviation of X.

 

A. 2

 

B. 4

 

C. 16

 

D. 1.5

σx = √4 = 2.00

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
106. Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of 10 customers or fewer arriving within a minute.

 

A. .9998

 

B. .9990

 

C. .0008

 

D. .0498

P(X ≤ 10) = 1 − P(X ≥ 11) = 1 − .0002 = .9998

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

107. Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of more than 7 customers arriving within a minute.

 

A. .0216

 

B. .0081

 

C. .0108

 

D. .0118

P(X ≥ 8) = .0081 + .0027 + .0008 + .0002 = .0118

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

 

 

 

 

108. Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of 3 customers arriving within a minute.

 

A. 1.00

 

B. .1494

 

C. .224

 

D. .3734

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

109. One die is thrown. What is the expected value of the number of dots on the top face of the die?

 

A. 1.0

 

B. 3.5

 

C. 4.0

 

D. 3.0

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
110. X has the following probability distribution.

Compute the expected value of X.

 

 

A. 1.3

 

B. 1.0

 

C. 2.4

 

D. 1.8

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

111. X has the following probability distribution P(X).

Compute the expected value of X.

 

 

A. 2.5

 

B. 1.0

 

C. 1.6

 

D. 0.6

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
112. X has the following probability distribution P(X).

Compute the variance value of X.

 

 

A. 1.58

 

B. .955

 

C. .912

 

D. .625

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

113. Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition, the number of defects per unit is distributed according to a Poisson distribution. What is the probability that there will be a total of 7 defects on four units?

 

A. .8750

 

B. .1221

 

C. .0573

 

D. .1396

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
114. Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition, the number of defects per unit is distributed according to a Poisson distribution. A batch has just been completed. What is the probability that the first three units manufactured in this batch will contain at least a total of 4 defects?

 

A. .8488

 

B. .7149

 

C. .1512

 

D. .2851

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution

 

 

 

 

 

 

 

 

115. Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition, the number of defects per unit is distributed according to a Poisson distribution. Determine the standard deviation of the number of defects for 32 units.

 

A. 2

 

B. 32

 

C. 64

 

D. 8

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities.
Topic: The Poisson Distribution
116. Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). Determine the expected number of heads.

 

A. 1.5

 

B. 1.0

 

C. 2.0

 

D. 1.1

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

117. Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). What is the variance for this distribution?

 

A. 1.5

 

B. 1.22

 

C. 0.75

 

D. 0.87

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions
118. Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). What is the standard deviation for this distribution?

 

A. 1.5

 

B. 1.22

 

C. 0.75

 

D. 0.87

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

119. If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw, how much would you expect to win on average?

 

A. $3

 

B. $2

 

C. $6

 

D. $9

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

120. A pharmaceutical company has determined that if a new cholesterol-reducing drug is manufactured (introduced to the market), the following probability distribution will describe the contribution of this drug to their profits during the next six months.

The company management has decided to market this product if the expected contribution to profit for the next six months is more than $1,000,000. Based on the information given above, should the company begin manufacturing the new drug? Explain your answer.

 

 

A. Yes, begin manufacturing.

 

B. No, do not begin manufacturing.

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

121. According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the probability that none of the individuals has group A blood.

 

A. .0041

 

B. .0410

 

C. .4000

 

D. .0467

P(x = 0) = .0467

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

122. According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the probability that exactly three of the individuals have group A blood.

 

A. .4000

 

B. .2765

 

C. .5875

 

D. .0041

P(x = 3) = .2765

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

123. According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the probability that at least 3 of the individuals have group A blood.

 

A. .8208

 

B. .5443

 

C. .4557

 

D. .1792

P(x ≥ 3) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = .4557

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

124. According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the mean number of individuals having group A blood.

 

A. 1.2

 

B. 1.55

 

C. 1.44

 

D. 2.4

μx = np = (6)(.4) = 2.4

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

 

 

 

 

 

125. According to data from the state blood program, 40 percent of all individuals have group A blood. Suppose that of six randomly selected individuals, three have group A blood. Would you believe the data from the state blood program?

 

A. Yes, probability is > .05.

 

B. Yes, probability is < .05.

 

C. No

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

126. A lawyer believes that the probability is .3 that she can win a discrimination suit. If she wins the case, she will make $400,000; but if she loses, she gets nothing. Assume that she has to spend $75,000 preparing the case. What is her expected gain?

 

A. $325,000

 

B. $45,000

 

C. $150,000

 

D. $22,500

μx = .7(−75,000) + .3(325,000) = −52,500 + 97,500 = 45,000

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

127. The internal auditor for your company believes that 10 percent of your invoices contain errors. To check this theory, 20 invoices are randomly selected, and 5 are found to have errors. What is the probability that of the 20 invoices selected, 5 or more would contain errors if the theory is valid?

 

 

A. .0433

 

B. .0319

 

C. .9567

 

D. .8660

P(x ≥ 5) = .0319 + .0089 + .0020 + .0004 + 0001 = .0433

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

128. An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that all five will be repaired on the same day?

 

A. .0010

 

B. .6328

 

C. .9990

 

D. .2373

P(x = 5) = .2373

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

129. An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that fewer than two troubles will be repaired on the same day?

 

A. .6328

 

B. .0010

 

C. .0156

 

D. .0146

P(x < 2) = P(x = 0) + P(x = 1) = .0156

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
130. An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that at least three troubles will be repaired on the same day?

 

A. .1035

 

B. .0376

 

C. .9624

 

D. .8965

P(x ≥ 3) = 1 − (P ≤ 2) = .8965

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

131. An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, find the mean number of troubles repaired on the same day.

 

A. 3.75

 

B. 0.94

 

C. 1.94

 

D. 2.50

μx = np = (5)(.75) = 3.75

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
132. The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. If you mail eight local letters, what is the probability that all of them will be delivered the next day?

 

A. 1.0

 

B. .4305

 

C. .8131

 

D. .5695

P(x = 8) = .4305

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

133. The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. If you mail eight local letters, what is the average number you expect to be delivered the next day?

 

A. 3.6

 

B. 4.0

 

C. 7.2

 

D. 2.7

μx = np = (8)(.9) = 7.2

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 1 Easy
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

 

 

 

 

 

134. The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. Calculate the standard deviation of the number delivered when 8 local letters are mailed.

 

A. .85

 

B. .72

 

C. 2.68

 

D. 2.83

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

135. The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. When there are 8 local letters mailed, what is the probability that the number delivered will be within 2 standard deviations of the mean?

 

A. .9950

 

B. .9619

 

C. .8131

 

D. .9996

P[σ = 7.2 ± 2(.85)] = P(σ = 7.2 ± 1.7) = P(5.5 ≤ x ≤8) = P(6 ≤ x ≤8) = .4305 + .3826 + .1488 = .9619

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
136. A car wash loses $30 on rainy days and makes $120 on days when it does not rain. If the probability of rain is 0.15, calculate expected profit for the car wash.

 

A. $90

 

B. $76.50

 

C. $106.50

 

D. $97.50

μx = (−30)(.15) + (120)(.85) = −4.50 + 102 = 97.50

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

 

137. An insurance company will insure a $75,000 particular make and model of car for its full value against theft at a premium of $1500 per year. Suppose that the probability that this particular automobile make and model will be stolen is 0.0075. Calculate the expected net profit for the insurance company.

 

A. $937.50

 

B. $551.25

 

C. $1488.75

 

D. $562.50

μx = (−73,500)(.0075) + (1500)(.9925) = −551.25 + 1488.75 = 937.50

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

138. An insurance company will insure a $75,000 particular automobile make and model for its full value against theft at a premium of $1500 per year. Suppose that the probability that this particular make and model will be stolen is 0.0075. Find the premium that the insurance company should charge if it wants its expected net profit to be $2000.

 

A. $1437.50

 

B. $2551.25

 

C. $2562.50

 

D. $2062.50

2000 = (x − 75,000)(.0075) + x(.9925) = .0075x − 562.5 + .9925x = 2562.5

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation.
Topic: Discrete Probability Distributions

 

139. A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, calculate the probability that exactly 4 of the jobs were not completed within the bid time.

 

A. .0081

 

B. .2401

 

C. .0113

 

D. .1361

P(x = 4) = .1361

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution
140. A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, calculate the mean number of jobs completed within the bid time.

 

A. 4.0

 

B. 2.4

 

C. 2.0

 

D. 5.6

μx = np = 8(.3) = 2.4

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

 

 

 

 

 

141. A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.

 

 

A. .6867

 

B. .7483

 

C. .5506

 

D. .8844

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-03 Use the binomial distribution to compute probabilities.
Topic: The Binomial Distribution

 

142. Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate the mean of the distribution.

 

A. 0.500

 

B. 0.333

 

C. 1.500

 

D. 3.000

n(r/N) = 3(5/10) = 1.5

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

143. Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate the standard deviation of the distribution.

 

A. 0.583

 

B. 0.764

 

C. 1.500

 

D. 0.778

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

144. If in a hypergeometric distribution r = 300, N = 600, and n = 30, estimate the binomial probability of success.

 

A. 0.500

 

B. 0.333

 

C. 0.083

 

D. 0.250

P = r/N = 300/600 = 0.500

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

 

 

 

145. Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the probability that all 3 of your DVDs will last at least three years?

0.7

Feedback: P(x = 3) = (9C3 × 1C0)/10C3 = 84/120 = .7

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution
146. Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the mean of the random variable x?

2.7

Feedback: Mean = n(r/N) = 3(9/10) = 2.7

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

147. Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the standard deviation of the random variable x?

0.46

Feedback:

N = 10,  n = 3,  r = 9

S2 = n × (r/N) × [1 − (r/N)]  × [(N − n)/(N − 1)] = (2.7 × .1 × .78) = .21

Therefore, standard deviation = s = √.21 = .46

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 2 Medium
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

148. Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What values of x are within two standard deviations of the mean?

2 and 3

Feedback: x = [2.7 ± 2(.46)] = (2.7 ± .92) = (1.78, 3.62)

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities.
Topic: The Hypergeometric Distribution

 

149. The yearly proportional return for stock G = x, the yearly proportional return for stock H = y, μx = .16, μy = .07, σx = .11, σy = .11, and σxy2 = .0321. Find the mean and standard deviation of the portfolio return: P = .45x + .55y.

mean = .1105; standard deviation = .148

Feedback:

μp = μ(.45x+.55y) = .45(.16) + .55(.07) = .110

σp = √[(.45)2(.11)2 + (.55)2(.11)2 + 2(.45)(.55)(.0321)] = √.022 = .148

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-06 Compute and understand the covariance between two random variables.
Topic: Joint Distributions and the Covariance
150. The yearly proportional return for stock G = x, the yearly proportional return for stock H = y, μx = .16, μy = .07, σx = .11, σy = .11, and σxy2 = .0321. Find the mean and standard deviation of the portfolio return: P = .5x + .5y.

mean = .115, standard deviation = .149

Feedback:

μp =  μ(.5x+.5y) = .5(.16) + .5(.07) = .115

σp = √[(.5)2(.11)2 + (.5)2(.11)2 + 2(.5)(.5)(.0321)] = √.0221 = .149

 

AACSB: Analytical Thinking
Blooms: Apply
Difficulty: 3 Hard
Learning Objective: 05-06 Compute and understand the covariance between two random variables.
Topic: Joint Distributions and the Covariance

 

 

 

Chapter 05 Test Bank – Static Summary

Category # of Questions
AACSB: Analytical Thinking 103
AACSB: Reflective Thinking 47
Blooms: Analyze 4
Blooms: Apply 100
Blooms: Evaluate 1
Blooms: Remember 36
Blooms: Understand 9
Difficulty: 1 Easy 29
Difficulty: 2 Medium 97
Difficulty: 3 Hard 24
Learning Objective: 05-01 Explain the difference between a discrete random variable and a continuous random variable. 6
Learning Objective: 05-02 Find a discrete probability distribution and compute its mean and standard deviation. 31
Learning Objective: 05-03 Use the binomial distribution to compute probabilities. 60
Learning Objective: 05-04 Use the Poisson distribution to compute probabilities. 32
Learning Objective: 05-05 Use the hypergeometric distribution to compute probabilities. 16
Learning Objective: 05-06 Compute and understand the covariance between two random variables. 5
Topic: Discrete Probability Distributions 29
Topic: Joint Distributions and the Covariance 5
Topic: The Binomial Distribution 61
Topic: The Hypergeometric Distribution 16
Topic: The Poisson Distribution 32
Topic: Two Types of Random Variables 7

 

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