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Statistical Techniques In Business and Economics 16th Edition by Lind – Test Bank

Chapter 06

Discrete Probability Distributions

True / False Questions

A random variable represents the outcome of an experiment.

True False

The probability of a particular outcome must always be between 0.0 and 1.0 inclusive.

True False

The random variable for a Poisson probability distribution can assume an infinite number of values.

True False

A probability distribution is a mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance, and their corresponding probabilities.

True False

To construct a binomial probability distribution, the mean must be known.

True False

To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial.

True False

The mean of a probability distribution is called its expected value.

True False

The variance of a probability distribution is based on the sum or squared differences from the mean.

True False

The variance measures the skewness of a probability distribution.

True False

10.

The mean of a binomial distribution is the product of n and π.

True False

11.

The variance of a binomial distribution is found by nπ(1 – π).

True False

12.

In a Poisson distribution, the probability of success may vary from trial to trial.

True False

13.

The binomial probability distribution is always negatively skewed.

True False

14.

When sampling is done without replacement and the outcomes are measured as either a success or failure, the hypergeometric distribution should be applied.

True False

15.

As a general rule of thumb, if the items selected for a sample are not replaced and the sample size is less than 5 percent of the population, the binomial distribution can be used to approximate the hypergeometric distribution.

True False

Multiple Choice Questions

16.

If the variance is 3.6 grams, what is the standard deviation?

0.600

1.897

6.000

12.96

17.

A total of 60% of the customers of a fast food chain order a hamburger, French fries, and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

1.000

0.186

0.403

0.000

18.

Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?

0.001

0.167

0.735

0.500

19.

The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is:

On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?

10.00

1.00

2.85

1.96

20.

On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?

0.002

0.344

0.599

0.100

21.

Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?

0.8187

0.2500

0.0164

0.0001

22.

A listing of all possible outcomes of an experiment and their corresponding probabilities of occurrence is called a ____________.

random variable

probability distribution

subjective probability

frequency distribution

23.

Which one of the following is NOT a condition of the binomial distribution?

Independent trials

Only two outcomes

The probability of success remains constant from trial to trial

Sampling at least 10 trials

24.

Which is true for a binomial distribution?

There are ten or more possible outcomes.

The probability of success remains the same from trial to trial.

The value of π is equal to 1.50.

It approximates the Poisson distribution.

25.

Which shape describes a Poisson distribution?

Positively skewed

Negatively skewed

Symmetrical

All apply

26.

Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50-50. If you bought 20 tickets, what is the chance of winning 15 or more prizes?

0.250

0.021

0.006

0.750

27.

What kind of distributions are the binomial and Poisson probability distributions?

Discrete

Continuous

Both discrete and continuous

Neither discrete or continuous

28.

Which of the following is correct about a probability distribution?

The sum of all possible outcomes must equal 1.0.

The outcomes must be mutually exclusive.

The probability of each outcome must be between 0.0 and 1.0 inclusive.

All apply.

29.

Data show that the weight of an offensive linesman may be any weight between 200 and 350 pounds. The distribution of weight is based on a ______________.

continuous random variable

discrete random variable

qualitative variable

All apply.

30.

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10% of the diamond wedding rings are returned. Five different customers buy a wedding ring. What is the probability that none of the customers return a ring?

0.250

0.073

0.590

0.500

31.

In a large metropolitan area, past records revealed that 30% of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

0.114

0.887

0.400

0.231

32.

Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?

0.900

0.031

0.001

0.250

33.

A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective cars. Some of the cars had no defects, a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 100 cars produced, about how many out of every 1,000 cars assembled should have one or more defects?

About 660

About 165

About 630

About 330

34.

The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixture or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two; and so on. The average number was 0.5 per door. The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes?

About 6,065

About 3,935

About 5,000

About 500

35.

A manufacturer of headache medicine claims it is 70% effective within a few minutes. That is, out of every 100 users, 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that eight have relief within a few minutes?

0.001

0.168

0.667

0.231

36.

A true/false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?

0.016

0.062

0.250

37.

A farmer who grows genetically engineered corn is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: Many of the ears contained no borers. Some ears had one borer; A few had two borers, and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The farmer counted 3,500 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers?

0.3476

0.4966

1.000

0.0631

38.

A tennis match requires that a player win three of five sets to win the match. If a player wins the first two sets, what is the probability that the player wins the match, assuming that each player is equally likely to win each set?

0.500

0.125

0.875

0.000

39.

A machine shop has 100 drill presses and other machines in constant use. The probability that a machine will become inoperative during a given day is 0.002. During some days, no machines are inoperative, but on other days, one, two, three, or more are broken down. What is the probability that fewer than two machines will be inoperative during a particular day?

0.0200

0.1637

0.8187

0.9824

40.

A coin is tossed four times. The following table summarizes the experiment. What is the following table called?

Probability distribution

Cumulative frequency distribution

Standard deviation

Frequency table

41.

What is the only variable in the Poisson probability formula?

42.

Which of the following is NOT a characteristic of a binomial probability distribution?

Each outcome is mutually exclusive.

Each trial is independent.

The probability of success remains constant from trial to trial.

The number of trials is limited to two.

43.

What must you know to develop a binomial probability distribution?

The probability of success

The probability of success and the number of trials

The probability of success and the number of successes

The number of trials and the number of successes

44.

To apply a Poisson probability distribution, the mean can be computed as __________.

nπ

e^-x

45.

In a Poisson distribution, the variance is equal to ___________.

nπ

e^-x

46.

David’s gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that at least 10 pay in cash?

0.024

0.033

0.009

0.976

47.

0.0

0.1

0.9

1.0

48.

0.210

0.212

0.092

0.562

49.

David’s gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. This situation is an example of what type of discrete probability distribution?

Continuous probability distribution

Poisson probability distribution

Binomial probability distribution

Hypergeometric probability distribution

50.

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have no messages?

0.0067

Zero

0.0335

Impossible to have no messages

51.

0.0067

0.8750

0.1755

1.0000

52.

0.0067

0.0014

0.4200

0.0842

53.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

What is the mean number of days absent?

1.00

0.40

0.72

2.5

54.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

What is the variance of the number of days absent?

1.1616

1.41

5.00

55.52

55.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

Given the probability distribution, which of the following predictions is correct?

60% of the employees will have more than one day absent per month.

There is a 0.04 probability that an employee will be absent one day per month.

There is a 0.12 probability that an employee will be absent two days per month.

There is a 0.50 probability that an employee will be absent 0.72 days per month.

56.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

What is the mode of the distribution?

0.72 days

2.5 days

0 days

3 days

57.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

What is the standard deviation of the number of days absent?

1.1616

1.6595

1.0778

58.

For the following distribution:

What is the mean of the distribution?

2.5

1.604

59.

For the following distribution:

What is the variance of the distribution?

1.1616

0.964

0.982

1.000

60.

For the following distribution:

What is the mean of the distribution?

2.1

1.5

0.441

61.

For the following distribution:

What is the variance of the distribution?

2.1

0.63

3.9

2.754

62.

For the following distribution:

What is the mean of the distribution?

2.1

1.13

0.113

1.5

63.

For the following distribution:

What is the variance of the distribution?

2.1

0.132

0.364

1.000

64.

The following is a binomial probability distribution with n = 3 and π = 0.20.

The mean of the distribution is _______.

1.50

0.60

0.25

0.00

65.

The following is a binomial probability distribution with n = 3 and π = 0.20.

The variance of the distribution is _________.

1.5

3.0

0.69

0.48

66.

The following is a Poisson probability distribution with µ = 0.1.

The mean of the distribution is _____.

1.5

0.1

0.25

1.0

67.

The following is a Poisson probability distribution with µ = 0.1.

The variance of the distribution is ______.

1.0

0.9046

3.0

0.1

68.

For a binomial distribution, the mean is 0.6 and n = 2. What is π for this distribution?

0.5

1.00

0.3

0.1

69.

For a binomial distribution, the mean is 4.0 and n = 8. What is π for this distribution?

0.5

1.00

4.0

0.1

70.

The marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favorite flake cereals. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person. The bowls were labeled A, B, C, D and E. The person was informed that only one bowl contained his or her favorite flake cereal. Suppose that the eight persons in the experiment were unable to identify their favorite cereal and just guessed which bowl it was in. What is the probability that none of the eight guessed correctly?

0.168

0.009

0.788

0.125

71.

An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?

0.250

0.500

0.410

0.026

72.

In which of the following discrete distribution does the probability of a success vary from one trial to the next?

Binomial

Poisson

Hypergeometric

All of these.

73.

Which of the following is a requirement for use of the hypergeometric distribution?

Only two possible outcomes

Trials are independent

Probability of a success is greater than 1.0

Sampling with replacement

74.

Affirmative action commitments by many organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives that it will fill from among four women and six men.
What is the probability that no woman is selected?

1/5

1/3

2/15

8/15

75.

8/15

3/5

2/3

3/4

76.

A type of probability distribution that shows the probability of x successes in n trials, where the probability of success remains the same from trial to trial, is referred to as a ___________.

hypergeometric probability distribution

uniform probability distribution

normal probability distribution

binomial probability distribution

77.

A measure of the long-run average value of a random variable used to represent the central location of a probability distribution is called a(n) _____________.

population variance

population standard deviation

expected value

coefficient of variation

78.

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a ___________.

discrete random variable

continuous random variable

complex random variable

simplex random variable

79.

The mean or expected value for a binomial probability distribution is _________.

μ = nπ(1 – π)

μ = π(1 – π)

μ = πn(1 – n)

μ = nπ

Fill in the Blank Questions

80.

For a trial, the number of possible outcomes for the binomial experiment is _____.

________________________________________

81.

A probability distribution is a listing of the expected outcomes of an experiment and the probability of each outcome occurring. The sum of the probabilities is ______.

________________________________________

82.

To construct a binomial distribution, we need to know the ___________ and the probability of a success.

________________________________________

83.

A probability distribution shows the outcomes of an experiment and the ___________________ of each one occurring.

________________________________________

84.

In a binomial experiment, the probability of a _________ remains constant.

________________________________________

85.

To do this, the _______ probability distribution should be applied.

________________________________________

86.

In a binomial experiment, the probability of a failure equals _________.

________________________________________

87.

A binomial probability distribution approaches a greater degree of symmetry as the probability of success remains constant and the number of trials becomes ___________.

________________________________________

88.

The Poisson distribution or, the law of improbable events, is _______________ skewed.

________________________________________

89.

If π = 1/3 and n = 900, the mean of this binomial distribution is ______.

________________________________________

90.

If π = 1/5 and n = 100, the standard deviation of this binomial distribution is _____.

________________________________________

91.

If n = 900 and π = ⅓, the variance of this binomial distribution is ______.

________________________________________

92.

A _______________ random variable can assume only a certain number of separated values.

________________________________________

93.

For any probability distribution, the mean is calculated as a weighted mean. The weights are the ______________.

________________________________________

94.

A probability distribution shows the distribution of a ______________.

________________________________________

95.

For any probability distribution, the standard deviation is the ______________.

________________________________________

96.

A continuous random variable can assume one of a(n) ____________ number of values within a specific range.

________________________________________

97.

A random variable with a Poisson distribution has one of _______ mutually exclusive values.

________________________________________

98.

In a Poisson distribution, each trial is ___________________.

________________________________________

99.

In a Poisson distribution, the mean and variance are ________________.

________________________________________

100.

In the _______________________ distribution, the probability of a success is not the same on each trail.

________________________________________

101.

For the hypergeometric distribution there are ________________ possible outcomes.

________________________________________

Short Answer Questions

102.

The mean of a binomial distribution is calculated using ____.

103.

The mean of a Poisson distribution is calculated using ____.

104.

Essay Questions

105.

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?

106.

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of four every five minutes, what is the probability that more than four customers arrive in a five-minute period?

107.

Elly’s Hotdog Emporium is famous for its chilidogs. Elly’s latest sales indicate that 30% of the customers order their chilidogs with hot peppers. Suppose 15 customers are selected at random. What is the probability that exactly 10 customers will ask for hot peppers?

108.

109.

110.

A company is studying the number of daily debit card purchases. There were 20 purchases and the probability of a debit card purchase is 0.5. Of the 20 purchases, what is the expected value of the number of debit card purchases?

111.

A company is studying the number of daily debit card purchases. There were 20 purchases and the probability of a debit card purchase is 0.5. What is the standard deviation of the number of debit card purchases?

112.

A company is studying the number of daily debit card purchases. There were 20 purchases and the probability of a debit card purchase is 0.5. Based on the shape of the distribution, approximately 99.7% of the purchases should be between _______ and ________.

113.