CHAPTER 5

DISCRETE DISTRIBUTIONS

CHAPTER LEARNING OBJECTIVES

1. Define a random variable in order to differentiate between a discrete distribution and a continuous distribution. Probability experiments produce random outcomes. A variable that contains the outcomes of a random experiment is called a random variable. Random variables such that the set of all possible values is at most a finite or countably infinite number of possible values are called discrete random variables. Random variables that take on values at all points over a given interval are called continuous random variables. Discrete distributions are constructed from discrete random variables. Continuous distributions are constructed from continuous random variables.

2. Determine the mean, variance, and standard deviation of a discrete distribution. The measures of central tendency and measures of variability discussed in Chapter 3 for grouped data can be applied to discrete distributions to compute a mean, a variance, and a standard deviation. Important examples of discrete distributions are the binomial distribution, the Poisson distribution, and the hypergeometric distribution.

3. Solve problems involving the binomial distribution using the binomial formula and the binomial table. The binomial distribution fits experiments when only two mutually exclusive outcomes are possible. In theory, each trial in a binomial experiment must be independent of the other trials. However, if the population size is large enough in relation to the sample size (n < 5%N), the binomial distribution can be used where applicable in cases where the trials are not independent. The probability of getting a desired outcome on any one trial is denoted as p, which is the probability of getting a success. The binomial distribution can be used to analyze discrete studies involving such things as heads/tails, defective/good, and male/female. The binomial formula is used to determine the probability of obtaining x outcomes in n trials. Binomial distribution problems can be solved more rapidly with the use of binomial tables than by formula. A binomial table can be constructed for every different pair of n and p values. Table A.2 of Appendix A contains binomial tables for selected values of n and p.

4. Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table. The Poisson distribution is usually used to analyze phenomena that produce rare occurrences. The only information required to generate a Poisson distribution is the long-run average, which is denoted by lambda (λ). The Poisson distribution pertains to occurrences over some interval. The assumptions are that each occurrence is independent of other occurrences and that the value of lambda remains constant throughout the experiment. Examples of Poisson-type experiments are number of flaws per page of paper and number of calls per minute to a switchboard. Poisson probabilities can be determined by either the Poisson formula or the Poisson tables in Table A.3 of Appendix A. The Poisson distribution can be used to approximate binomial distribution problems when n is large (n > 20), p is small, and n • p ≤ 7.

5. Solve problems involving the hypergeometric distribution using the hypergeometric formula. The hypergeometric distribution is a discrete distribution that is usually used for binomial-type experiments when the population is small and finite and sampling is done without replacement. Because using the hypergeometric distribution is a tedious process, using the binomial distribution whenever possible is generally more advantageous.

TRUE-FALSE STATEMENTS

1. Variables which take on values only at certain points over a given interval are called continuous random variables.

Difficulty: Easy

Learning Objective: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Section Reference: 5.1 Discrete versus Continuous Distributions

Bloom’s: Knowledge

AACSB: Analytic

2. A variable that can take on values at any point over a given interval is called a discrete random variable.

Difficulty: Easy

Learning Objective: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Section Reference: 5.1 Discrete versus Continuous Distributions

Bloom’s: Knowledge

AACSB: Analytic

3. The number of automobiles sold by a dealership in a day is an example of a discrete random variable.

Difficulty: Easy

Learning Objective: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Section Reference: 5.1 Discrete versus Continuous Distributions

Bloom’s: Knowledge

AACSB: Analytic

4. The amount of time a patient waits in a doctor's office is an example of a continuous random variable.

Difficulty: Easy

Learning Objective: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Section Reference: 5.1 Discrete versus Continuous Distributions

Bloom’s: Knowledge

AACSB: Analytic

5. The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Knowledge

AACSB: Analytic

6. To compute the variance of a discrete distribution, it is not necessary to know the mean of the distribution.

Difficulty: Medium

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Comprehension

AACSB: Reflective Thinking

7. In a binomial experiment, any single trial contains only two possible outcomes and successive trials are dependent.

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Comprehension

AACSB: Analytic

8. In a binomial distribution, p, the probability of getting a successful outcome on any single trial, remains the same from one trial to another.

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Knowledge

AACSB: Analytic

9. The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20 of the population size.

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Knowledge

AACSB: Analytic

10. For a binomial distribution in which the probability of success p = 0.5, the variance is twice the mean.

Difficulty: Hard

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Analysis

AACSB: Analytic

11. The Poisson distribution is a discrete distribution.

Difficulty: Easy

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Knowledge

AACSB: Analytic

12. Both the Poisson and the binomial distributions are discrete distributions and both have a given number of trials.

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Comprehension

AACSB: Reflective Thinking

13. The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

Difficulty: Easy

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Knowledge

AACSB: Reflective Thinking

14. For the Poisson distribution, the mean and the standard deviation are the same.

Difficulty: Easy

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Knowledge

AACSB: Analytic

15. A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Saint Lawrence.

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Comprehension

AACSB: Reflective Thinking

16. For the Poisson distribution, the mean and the variance are the same.

Difficulty: Easy

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Knowledge

AACSB: Analytic

17. Poisson distribution describes the occurrence of discrete events that may occur over a continuous interval of time or space.

Difficulty: Hard

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Synthesis

AACSB: reflective Thinking

18. A hypergeometric distribution applies to experiments in which the trials represent sampling without replacement.

Difficulty: Easy

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Knowledge

AACSB: Analytic

19. As in a binomial distribution, each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes, i.e., either a success or a failure.

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Comprehension

AACSB: Analytic

20. As in a binomial distribution, successive trials of a hypergeometric distribution are independent.

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Synthesis

AACSB: Reflective Thinking

MULTIPLE CHOICE QUESTIONS

21. The volume of liquid in an unopened 1-litre can of paint is an example of ___.

a) the binomial distribution

b) the normal distribution

c) a continuous random variable

d) a discrete random variable

e) a constant

Difficulty: Easy

Learning Objective: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Section Reference: 5.1 Discrete versus Continuous Distributions

Bloom’s: Comprehension

AACSB: Analytic

22. The number of defective parts in a lot of 25 parts is an example of ___.

a) a discrete random variable

b) a continuous random variable

c) the Poisson distribution

d) the normal distribution

e) a constant

Difficulty: Easy

Learning Objective: Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Section Reference: 5.1 Discrete versus Continuous Distributions

Bloom’s: Comprehension

AACSB: Analytic

23. You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table:

The mean of this distribution is ___.

a) -$400

b) $0

c) $200

d) $400

e) $500

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Application

AACSB: Analytic

24. You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table:

The standard deviation of this distribution is ___.

a) -$400

b) $663

c) $800,000

d) $894

e) $2000

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Analysis

AACSB: Analytic

25. You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table:

Which of the following statements is true?

a) This distribution is skewed to the right.

b) This is a binomial distribution.

c) This distribution is symmetric.

d) This distribution is skewed to the left.

e) This is a Poisson distribution

Difficulty: Medium

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Evaluation

AACSB: Reflective Thinking

26. A market research team compiled the following discrete probability distribution. In this distribution x represents the number of automobiles owned by a family.

The mean (average) value of x is ___.

a) 1.0

b) 1.5

c) 2.0

d) 2.5

e) 3.0

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Application

AACSB: Analytic

27. A market research team compiled the following discrete probability distribution. In this distribution x represents the number of automobiles owned by a family.

The standard deviation of x is ___.

a) 0.80

b) 0.89

c) 1.00

d) 2.00

e) 2.25

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Analysis

AACSB: Analytic

28. A market research team compiled the following discrete probability distribution. In this distribution x represents the number of automobiles owned by a family.

Which of the following statements is true?

a) This distribution is skewed to the right.

b) This is a binomial distribution.

c) This is a normal distribution.

d) This distribution is skewed to the left.

e) This distribution is bimodal.

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Synthesis

AACSB: Reflective Thinking

29. A market research team compiled the following discrete probability distribution for families residing in Randolph County. In this distribution x represents the number of evenings the family dines outside their home during a week.

The mean (average) value of x is ___.

a) 1.0

b) 1.5

c) 2.0

d) 2.5

e) 3.0

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Application

AACSB: Analytic

30. A market research team compiled the following discrete probability distribution for families residing in Randolph County. In this distribution x represents the number of evenings the family dines outside their home during a week.

The standard deviation of x is ___.

a) 1.00

b) 2.00

c) 0.80

d) 0.89

e) 1.09

Difficulty: Easy

Learning Objective: Determine the mean, variance, and standard deviation of a discrete distribution.

Section Reference: 5.2 Describing a Discrete Distribution

Bloom’s: Analysis

AACSB: Analytic, Diversity

31. A Bernoulli process (each trial) has exactly ___ possible outcomes.

a) 8

b) 4

c) 2

d) 1

e) 6

Difficulty: Easy

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Knowledge

AACSB: Analytic

32. If x is the number of successes in an independent series of 10 trials, then x has a ___ distribution.

a) hypergeometric

b) Poisson

c) normal

d) binomial

e) exponential

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Comprehension

AACSB: Analytic

33. If x has a binomial distribution with p = .5, then the distribution of x is ___.

a) skewed to the right

b) skewed to the left

c) symmetric

d) a Poisson distribution

e) a hypergeometric distribution

Difficulty: Easy

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Comprehension

AACSB: Reflective Thinking

34. The following graph is a binomial distribution with n = 6:

This graph reveals that ___.

a) p > 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Evaluation

AACSB: Reflective Thinking

35. The following graph is a binomial distribution with n = 6:

This graph reveals that ___.

a) p > 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Evaluation

AACSB: Reflective Thinking

36. The following graph is a binomial distribution with n = 6:

This graph reveals that ___.

a) p = 0.5

b) p = 1.0

c) p = 0

d) p < 0.5

e) p = 1.5

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Analysis

AACSB: Reflective Thinking

37. Twenty five items are sampled. Each of these has the same probability of being defective. The probability that exactly 2 of the 25 are defective could best be found by ___.

a) using the normal distribution

b) using the binomial distribution

c) using the Poisson distribution

d) using the exponential distribution

e) using the uniform distribution

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Comprehension

AACSB: Analytic

38. A fair coin is tossed 5 times. What is the probability that exactly 2 heads are observed?

a) 0.313

b) 0.073

c) 0.400

d) 0.156

e) 0.250

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic

39. A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?

a) 0.200

b) 0.031

c) 0.156

d) 0.073

e) 0.001

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic

40. A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions?

a) 0.000

b) 0.200

c) 0.500

d) 0.031

e) 1.000

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic

41. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contain errors, P(x = 0) is ___.

a) 0.8171

b) 0.1074

c) 0.8926

d) 0.3020

e) 0.2000

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic, Ethics

42. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contain errors, P(x>0) is ___.

a) 0.8171

b) 0.1074

c) 0.8926

d) 0.3020

e) 1.0000

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Analysis

AACSB: Analytic, Ethics

43. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors, the mean value of x is ___.

a) 400

b) 2

c) 200

d) 5

e) 1

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic, Ethics

44. Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013. A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contains errors, the standard deviation of x is ___.

a) 1.26

b) 1.60

c) 14.14

d) 3.16

e) 0.00

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic, Ethics

45. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0) is ___.

a) 0.8154

b) 0.0467

c) 0.0778

d) 0.4000

e) 0.5000

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic, Ethics

46. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x<2) is ___.

a) 0.3370

b) 0.9853

c) 0.9785

d) 0.2333

e) 0.5000

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Analysis

AACSB: Analytic, Ethics

47. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x>0) is ___.

a) 0.2172

b) 0.9533

c) 0.1846

d) 0.9222

e) 1.0000

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Analysis

AACSB: Analytic, Ethics

48. Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number on non-authentic names in her sample, the expected (average) value of x is ___.

a) 2.50

b) 2.00

c) 1.50

d) 1.25

e) 1.35

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic, Ethics

49. If x is a binomial random variable with n=8 and p=0.6, the mean value of x is ___.

a) 6

b) 4.8

c) 3.2

d) 8

e) 48

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic

50. If x is a binomial random variable with n=8 and p=0.6, the standard deviation of x is ___.

a) 4.8

b) 3.2

c) 1.92

d) 1.39

e) 1.00

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic

51. If x is a binomial random variable with n=8 and p=0.6, what is the probability that x is equal to 4?

a) 0.500

b) 0.005

c) 0.124

d) 0.232

e) 0.578

Difficulty: Medium

Learning Objective: Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Section Reference: 5.3 Binomial Distribution

Bloom’s: Application

AACSB: Analytic

52. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is ___.

a) 0.0940

b) 0.0417

c) 0.1500

d) 0.1008

e) 0.2890

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Application

AACSB: Analytic

53. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 3 cars arriving over a five-minute interval is ___.

a) 0.2700

b) 0.0498

c) 0.2240

d) 0.0001

e) 0.0020

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Application

AACSB: Analytic

54. For the Poisson distribution of a random variable lambda (λ) is 5 occurrences per ten-minute time interval. If we want to analyze the number of occurrences per hour, we must use an adjusted value for lambda equal to ___.

a) 5

b) 60

c) 30

d) 10

e) 20

Difficulty: Easy

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Application

AACSB: Analytic

55. On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen-minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is ___.

a) 0.1008

b) 0.0361

c) 0.1339

d) 0.1606

e) 0.5000

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Application

AACSB: Analytic

56. On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next five minute interval is ___.

a) 0.1008

b) 0.0361

c) 0.1339

d) 0.1606

e) 0.3610

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Analysis

AACSB: Analytic

57. The Poisson distribution is being used to approximate a binomial distribution. If n=40 and p=0.06, what value of lambda would be used?

a) 0.06

b) 2.4

c) 0.24

d) 24

e) 40

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Application

AACSB: Analytic

58. The Poisson distribution is being used to approximate a binomial distribution. If n=60 and p=0.02, what value of lambda would be used?

a) 0.02

b) 12

c) 0.12

d) 1.2

e) 120

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Application

AACSB: Analytic

59. The number of phone calls arriving at a switchboard in a 10 minute time period would best be modelled with the ___.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Comprehension

AACSB: Analytic, Technology

60. The number of defects per 1,000 feet of extruded plastic pipe is best modelled with the ___.

a) Poisson distribution

b) Pascal distribution

c) binomial distribution

d) hypergeometric distribution

e) exponential distribution

Difficulty: Medium

Learning Objective: Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Section Reference: 5.4 Poisson Distribution

Bloom’s: Comprehension

AACSB: Reflective Thinking

61. The hypergeometric distribution is similar to the binomial distribution except that ___.

a) sampling is done with replacement in the hypergeometric

b) sampling is done without replacement in the hypergeometric

c) x does not represent the number of successes in the hypergeometric

d) there are more than two possible outcomes in the hypergeometric

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Synthesis

AACSB: Reflective Thinking

62. The probability of selecting 2 male employees and 3 female employees for promotions in a small company would best be modelled with the ___.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Comprehension

AACSB: Analytic, Diversity

63. The probability of selecting 3 defective items and 7 good items from a warehouse containing 10 defective and 50 good items would best be modelled with the ___.

a) binomial distribution

b) hypergeometric distribution

c) Poisson distribution

d) hyperbinomial distribution

e) exponential distribution

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Comprehension

AACSB: Analytic

64. Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women. What is the probability that all three people selected are men?

a) 0.05

b) 0.33

c) 0.11

d) 0.80

e) 0.90

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Diversity

65. Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women. What is the probability that one man and two women are selected?

a) 0.15

b) 0.06

c) 0.33

d) 0.48

e) 0.58

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Diversity

66. Aluminum castings are processed in lots of five each. A sample of two castings is randomly selected from each lot for inspection. A particular lot contains one defective casting; and x is the number of defective castings in the sample. P(x=0) is ___.

a) 0.2

b) 0.4

c) 0.6

d) 0.8

e) 1.0

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Technology

67. Aluminum castings are processed in lots of five each. A sample of two castings is randomly selected from each lot for inspection. A particular lot contains one defective casting; and x is the number of defective castings in the sample. P(x=1) is ___.

a) 0.2

b) 0.4

c) 0.6

d) 0.8

e) 1.0

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Technology

68. Circuit boards for wireless telephones are etched in an acid bath, in batches of 100 boards. A sample of seven boards is randomly selected from each lot for inspection. A batch contains two defective boards; and x is the number of defective boards in the sample. P(x=1) is ___.

a) 0.1315

b) 0.8642

c) 0.0042

d) 0.6134

e) 0.6789

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Technology

69. Circuit boards for wireless telephones are etched in an acid bath, in batches of 100 boards. A sample of seven boards is randomly selected from each lot for inspection. A particular batch contains two defective boards; and x is the number of defective boards in the sample. P(x=2) is ___.

a) 0.1315

b) 0.8642

c) 0.0042

d) 0.6134

e) 0.0034

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Technology

70. Circuit boards for wireless telephones are etched in an acid bath, in batches of 100 boards. A sample of seven boards is randomly selected from each lot for inspection. A particular batch contains two defective boards; and x is the number of defective boards in the sample. P(x=0) is ___.

a) 0.1315

b) 0.8642

c) 0.0042

d) 0.6134

e) 0.8134

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Technology

71. Ten policyholders file claims with CareFree Insurance. Three of these claims are fraudulent. Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample, P(x=0) is ___.

a) 0.0083

b) 0.3430

c) 0.0000

d) 0.2917

e) 0.8917

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Ethics

72. Ten policyholders file claims with CareFree Insurance. Three of these claims are fraudulent. Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample, P(x=1) is ___.

a) 0.5250

b) 0.4410

c) 0.3000

d) 0.6957

e) 0.9957

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Analysis

AACSB: Analytic, Ethics

73. If sampling is performed without replacement, the hypergeometric distribution should be used. However, the binomial may be used to approximate this if ___.

a) n > 5%N

b) n < 5%N

c) the population size is very small

d) there are more than two possible outcomes of each trial

e) the outcomes are continuous

Difficulty: Hard

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Synthesis

AACSB: Reflective Thinking

74. One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the ten claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample, x has a ___ distribution.

a) continuous

b) normal

c) binomial

d) hypergeometric

e) exponential

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Evaluation

AACSB: Ethics, Reflective Thinking

75. One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the ten claims for thorough investigation. If x represents the number of fraudulent claims in Earl's sample, x has a ___.

a) normal distribution

b) hypergeometric distribution, but may be approximated by a binomial

c) binomial distribution, but may be approximated by a normal

d) binomial distribution, but may be approximated by a Poisson

e) exponential distribution

Difficulty: Medium

Learning Objective: Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Section Reference: 5.5 Hypergeometric Distribution

Bloom’s: Evaluation

AACSB: Ethics, Reflective Thinking

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