Exam Prep Ch6 Discrete Probability Distributions

Basic Statistics for Business and Economics, 9e (Lind)

Chapter 6 Discrete Probability Distributions

1) A random variable is measured or observed as the result of an experiment.

2) The probability of a particular outcome is between 0 and 1 inclusive.

3) The random variable x for a Poisson distribution can assume an infinite number of values.

4) A probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome.  The outcomes are mutually exclusive, and the list of outcomes is exhaustive.

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

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

7) The mean of a probability distribution is also referred to as its expected value.

8) The variance of a probability distribution is the sum of the products of the squared differences (the mean subtracted from each random variable), multiplied by the  probability of each specific corresponding random variable.

9) The variance measures the skewness of a probability distribution.

10) The mean of a binomial distribution can be computed in a "shortcut" fashion by multiplying n (the total number of trials) times π (the probability of success).

11) The variance of a binomial distribution can be computed in a "shortcut" fashion by multiplying n (the total number of trials), times π (the probability of success), times (1 − π). (the probability of failure).

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

13) The binomial probability distribution is always negatively skewed.

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

A) 0.600

B) 1.897

C) 6.000

D) 12.96

15) 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?

A) 1.000

B) 0.186

C) 0.403

D) 0.000

16) 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?

A) 0.001

B) 0.167

C) 0.735

D) 0.500

17) 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?

A) 10.00

B) 1.00

C) 2.85

D) 1.96

18) 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?

A) 0.002

B) 0.344

C) 0.599

D) 0.100

19) 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?

A) 0.8187

B) 0.2500

C) 0.0164

D) 0.0001

20) A listing of all the outcomes of an experiment and the probability associated with each outcome is called a ________.

A) random variable

B) probability distribution

C) subjective probability

D) frequency distribution

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

A) Independent trials.

B) Only two outcomes.

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

D) Sampling at least 10 trials.

22) Which of the following is true for a binomial distribution?

A) There are 10 or more possible outcomes.

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

C) The value of π is equal to 1.50.

D) It approximates the Poisson distribution.

23) Which of the following shapes describes a Poisson distribution?

A) Positively skewed

B) Negatively skewed

C) Symmetrical

D) All of these answers are correct.

24) Which of the following is correct about a probability distribution?

A) The sum of all possible outcomes must equal 1.0.

B) The outcomes must be mutually exclusive.

C) The probability of each outcome must be between 0 and 1 inclusive.

D) All of these answers are correct.

25) 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 ________.

A) continuous random variable

B) discrete random variable

C) qualitative variable

D) all of these answers are correct.

26) 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?

A) 0.250

B) 0.073

C) 0.590

D) 0.500

27) 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?

A) 0.114

B) 0.887

C) 0.400

D) 0.231

28) 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?

A) 0.900

B) 0.031

C) 0.001

D) 0.250

29) 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?

A) About 660

B) About 165

C) About 630

D) About 330

30) 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?

A) About 6,065

B) About 3,935

C) About 5,000

D) About 500

31) 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?

A) 0.001

B) 0.168

C) 0.667

D) 0.231

32) 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?

A) 0

B) 0.016

C) 0.062

D) 0.250

33) 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?

A) 0.3476

B) 0.4966

C) 1.0000

D) 0.0631

34) 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?

A) 0.500

B) 0.125

C) 0.875

D) 0.000

35) 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?

A) 0.0200

B) 0.1637

C) 0.8187

D) 0.9824

36) A coin is tossed three times. The following table summarizes the experiment. How is the following table called?

A) Probability distribution.

B) Cumulative frequency distribution.

C) Standard deviation.

D) Frequency table.

37) What is the only variable in the Poisson probability formula?

A) π

B) x

C) e

D) P

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

A) Each outcome is mutually exclusive (i.e. classified as either a success or a failure).

B) Each trial is independent.

C) The probability of success is the same for each trial.

D) The number of trials is limited to two.

39) What must you know to construct a particular binomial probability?

A) The probability of success

B) The probability of success and the number of trials

C) The probability of success and the number of successes

D) The number of trials and the number of successes

40) The mean of a Poisson probability distribution can be computed as ________

A) nπ

B)

C) e −x

D)

41) The variance of a Poisson distribution is equal to ________.

A) nπ

B)

C) e −x

D)

42) David's gasoline station offers 4 cents off per gallon if the customer pays in cash. 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?

A) 0.024

B) 0.033

C) 0.009

D) 0.976

43) David's gasoline station offers 4 cents off per gallon if the customer pays in cash. 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 all 15 pay in cash?

A) 0.0

B) 0.1

C) 0.9

D) 1.0

44) David's gasoline station offers 4 cents off per gallon if the customer pays in cash. 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 more than 8 and less than 12 customers pay in cash?

A) 0.210

B) 0.212

C) 0.092

D) 0.562

45) David's gasoline station offers 4 cents off per gallon if the customer pays in cash. 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?

A) Continuous probability distribution

B) Poisson probability distribution

C) Binomial probability distribution

D) Hypergeometric probability distribution

46) 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?

A) 0.0067

B) 0

C) 0.0335

D) Impossible to have no messages

47) 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 five messages?

A) 0.0067

B) 0.8750

C) 0.1755

D) 1.0000

48) 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 two messages?

A) 0.0067

B) 0.0014

C) 0.4200

D) 0.0842

49) 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?

A) 1.00

B) 0.40

C) 0.72

D) 2.50

50) 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?

A) 1.1616

B) 1.41

C) 5.00

D) 55.52

51) 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?

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

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

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

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

52) 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?

A) 0.72 days

B) 2.5 days

C) 0 days

D) 3 days

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 standard deviation of the number of days absent?

A) 1.1616

B) 0

C) 1.6595

D) 1.0778

54) For the following distribution:

What is the mean of the distribution?

A) 1.0

B) 2.5

C) 1.6

D) 3.0

55) For the following distribution:

What is the variance of the distribution?

A) 1.161

B) 0.964

C) 0.982

D) 1.000

56) For the following distribution:

What is the mean of the distribution?

A) 2.100

B) 1.500

C) 0.441

D) 2.000

57) For the following distribution:

What is the variance of the distribution?

A) 2.10

B) 0.63

C) 3.90

D) 2.754

58) For the following distribution:

What is the mean of the distribution?

A) 2.100

B) 1.130

C) 0.113

D) 1.500

59) For the following distribution:

What is the variance of the distribution?

A) 2.100

B) 0.132

C) 0.364

D) 1.000

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

The mean of the distribution is ________.

A) 1.50

B) 0.60

C) 0.25

D) 0.00

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

The variance of the distribution is ________.

A) 1.50

B) 3.00

C) 0.69

D) 0.48

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

The mean of the distribution is ________.

A) 1.50

B) 0.10

C) 0.25

D) 1.00

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

The variance of the distribution is ________.

A) 1.0000

B) 0.9046

C) 3.0000

D) 0.1000

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

A) 0.50

B) 1.00

C) 0.30

D) 0.10

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

A) 0.50

B) 1.00

C) 4.00

D) 0.10

66) 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. In the survey, eight people were presented with five bowls of flake cereal, and were told that only one contained their favorite. 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?

A) 0.168

B) 0.009

C) 0.788

D) 0.125

67) 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 one out of five. Using the rules of probability, what is the likelihood that the agent will sell a policy to three of the four prospective clients?

A) 0.250

B) 0.500

C) 0.410

D) 0.026

68) 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(n) ________.

A) hypergeometric probability distribution

B) uniform probability distribution

C) normal probability distribution

D) binomial probability distribution

69) The long-run average value of a random variable used to represent the central location of a probability distribution is sometimes referred to as ________.

A) population variance

B) population standard deviation

C) expected value

D) coefficient of variation

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

A) discrete random variable

B) continuous random variable

C) complex random variable

D) simplex random variable

71) The mean or expected value for a binomial probability distribution is ________.

A) μ = nπ(1 − π)

B) μ = π(1 − π)

C) μ = πn(1 − n)

D) μ = nπ