- If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is
| a. larger than the probability of tails. |
| b. 0. |
| c. 1/2. |
| d. 1/16. |
2. The intersection of two mutually exclusive events
| a. can be any positive value. |
| b. can be any value between 0 to1. |
| c. must always be equal to 0. |
| d. must always be equal to 1. |
3. Two events with nonzero probabilities
| a. can not be both mutually exclusive and independent. |
| b. are always independent. |
| c. are always mutually exclusive. |
| d. can be both mutually exclusive and independent. |
4. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∩ B) =
| a. 0.00. |
| b. 0.15. |
| c. 0.20. |
| d. 0.30. |
5. A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial
| a. tail can not appear. |
| b. head has a larger chance of appearing than tail. |
| c. tail has same chance of appearing as the head. |
| d. tail has a better chance of appearing than head. |
6. A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the
| a. objective method. |
| b. experimental method. |
| c. subjective method. |
| d. classical method. |
7. If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A | B) =
| a. 0.45 |
| b. 0.40 |
| c. 0.22 |
| d. 0.00 |
8. The sample space refers to
| a. the sample size minus one. |
| b. any particular experimental outcome. |
| c. an event. |
| d. the set of all possible experimental outcomes |
9. Two events are mutually exclusive
| a. if most of their sample points are in common. |
| b. if their intersection is 0.5. |
| c. if their intersection is 1. |
| d. if they have no sample points in common |
10. Two events are mutually exclusive
| a. if most of their sample points are in common. |
| b. if their intersection is 0.5. |
| c. if their intersection is 1. |
| d. if they have no sample points in common |
11. The intersection of two mutually exclusive events
| a. must always be equal to 1. |
| b. must always be equal to 0. |
| c. can be any value between 0 to1. |
| d. can be any positive value. |
12. If X and Y are mutually exclusive events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =
| a. 0.6150. |
| b. 0.0000. |
| c. 1.0000. |
| d. 0.0944. |
13. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The union of A and B is
| a. all new customers. |
| b. all accounts from new customers and all accounts that are from 31 to 60 days past due. |
| c. all new customers whose accounts are between 31 and 60 days past due. |
| d. all accounts fewer than 31 or more than 60 days past due. |
14. Let F be the event that a customer is dissatisfied with the food at a restaurant and let S be the event that a customer is dissatisfied with the service. If P(F) = .15, P(S) = .40, and P(F ∩ S) = .10, what is the probability that a customer is dissatisfied with either the service or the food?
| a. .65 |
| b. .45 |
| c. .55 |
| d. .10 |
15. The complement of P(A | B) is
| a. P(A | BC). |
| b. P(B | A). |
| c. P(A I B). |
| d. P(AC | B). |
16. Each individual outcome of an experiment is called
| a. a trial. |
| b. a sample point. |
| c. the sample space. |
| d. an event. |
17. Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?
| a. 4/52 |
| b. 1/52 |
| c. 2/52 |
| d. 3/52 |
18. If P(A) = 0.62, P(B) = 0.56, and P(A ∪ B) = 0.70, then P(B | A) =
| a. .9032. |
| b. .7742. |
| c. .4800. |
| d. .3472. |
19. If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =
| a. 0.59. |
| b. 0.43. |
| c. 0.75. |
| d. 0.14. |
20. A description of the distribution of the values of a random variable and their associated probabilities is called a
| a. probability distribution. |
| b. table of binomial probability. |
| c. empirical discrete distribution. |
| d. bivariate distribution. |
21. The expected value for a binomial distribution is given by equation
| a. n(1 – p). |
| b. np. |
| c. (n – 1)(1 – p). |
| d. (n – 1)p. |
22. Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. The probability that the sample contains 2 female voters is
| a. 0.0778 |
| b. 0.3456 |
| c. 0.7780 |
| d. 0.5000 |
23. The student body of a large university consists of 60% female students. A random sample of 8 students is selected. What is the probability that among the students in the sample exactly two are female?
| a. 0.0007 |
| b. 0.2936 |
| c. 0.0413 |
| d. 0.0896 |
24. A weighted average of the values of a random variable, where the probability function provides weights, is known as
| a. the probable value. |
| b. the median value. |
| c. the variance. |
| d. the expected value. |
25. To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the
| a. exponential probability distribution. |
| b. hypergeometric probability distribution. |
| c. binomial probability distribution. |
| d. Poisson probability distribution |
26. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
| a. 0.0142 |
| b. 0.7408 |
| c. 0.9588 |
| d. 0.2592 |
27. The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Which of the following discrete probability distributions’ properties are satisfied by random variable x?
| a. Binomial |
| b. Hypergeometric |
| c. Normal |
| d. Poisson |
28. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a
| a. mixed type random variable. |
| b. multivariate random variable. |
| c. discrete random variable. |
| d. continuous random variable. |
29. In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the
| a. Poisson distribution. |
| b. Uniform distribution. |
| c. Binomial distribution. |
| d. Normal distribution. |
30. Assume the number of customers who order a dessert with their meal on a given night at a local restaurant has the probability distribution given below.
The variance for the random variable x is _____.
| a. .36 |
| b. .60 |
| c. 4 |
| d. .77 |
31. The following represents the probability distribution for the daily demand of computers at a local store.
| Demand | Probability |
| 0 | 0.1 |
| 1 | 0.2 |
| 2 | 0.3 |
| 3 | 0.2 |
| 4 | 0.2 |
The expected daily demand is
| a. 2.0 |
| b. 4.0 |
| c. 2.2 |
| d. 1.0 |
32. In a binomial experiment
| a. the probability changes from trial to trial. |
| b. the probability could change from trial to trial, depending on the situation under consideration. |
| c. the probability does not change from trial to trial. |
| d. the probability could change depending on the number of outcomes. |
33. In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is
| a. 5 |
| b. 6 |
| c. 2 |
| d. 10 |
34. Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.
| Production | |
| Per Month | Probability |
| 1 | 0.01 |
| 2 | 0.04 |
| 3 | 0.10 |
| 4 | 0.80 |
| 5 | 0.05 |
The expected monthly production level is
| a. 3.84 |
| b. 3.00 |
| c. 1.00 |
| d. 4.00 |
35. In a Poisson probability problem, the rate of defects is one every two hours. To find the probability of three defects in four hours,
| a. μ = 4, x = 3 |
| b. μ = 3, x = 4 |
| c. μ = 2, x = 3 |
| d. μ = 1, x = 4 |
36. A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
| a. 0.10 |
| b. 0.0004 |
| c. 0.02 |
| d. 0.0038 |
37. Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is
| a. 16. |
| b. 20. |
| c. 4. |
| d. 2. |
38. The probability distribution for the number of goals the Lions soccer team makes per game is given below.
| Number of Goals | Probability | |
| 0 | 0.05 | |
| 1 | 0.15 | |
| 2 | 0.35 | |
| 3 | 0.30 | |
| 4 | 0.15 |
What is the probability that in a given game the Lions will score less than 3 goals?
| a. .55 |
| b. .85 |
| c. .45 |
| d. .80 |
39. In a Poisson probability problem, the rate of defects is one every two hours. To find the probability of three defects in four hours,
| a. μ = 2, x = 3 |
| b. μ = 4, x = 3 |
| c. μ = 1, x = 4 |
| d. μ = 3, x = 4 |
40. The variance Var(x) for the binomial distribution is given by equation
| a. np(1 – np). |
| b. n(1 – p). |
| c. np(n – 1). |
| d. np(1 – p). |
41. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a
| a. discrete random variable. |
| b. multivariate random variable. |
| c. continuous random variable. |
| d. mixed type random variable. |
42. The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are less than 3 occurrences is
| a. .1239 |
| b. .1016 |
| c. .0659 |
| d. .0948 |
43. An air traffic controller has noted that it clears an average of seven planes per hour for landing. What is the probability that during the next two hours exactly 15 planes will be cleared for landing?
| a. .0033 |
| b. .0651 |
| c. .0989 |
| d. Not enough information is given to answer the question. |
44. Using a hypergeometric distribution with N = 6 and r = 2, what is the probability for n = 4 and x = 0?
| a. .6667 |
| b. .0667 |
| c. .0001 |
| d. .9333 |
45. The Poisson probability distribution is a
| a. continuous probability distribution. |
| b. normal probability distribution. |
| c. discrete probability distribution. |
| d. uniform probability distribution. |
46. In a Poisson probability problem, the rate of defects is one every two hours. To find the probability of three defects in four hours,
| a. μ = 2, x = 3 |
| b. μ = 4, x = 3 |
| c. μ = 1, x = 4 |
| d. μ = 3, x = 4 |
47. A binomial probability distribution with p = .3 is
| a. positively skewed. |
| b. multi-modal. |
| c. symmetric. |
| d. negatively skewed |
48. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
| a. 0.2592 |
| b. 0.0142 |
| c. 0.9588 |
| d. 0.7408 |
49. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a
| a. multivariate random variable. |
| b. mixed type random variable. |
| c. discrete random variable. |
| d. continuous random variable. |
50. The probability distribution for the daily sales at Michael’s Co. is given below.
| Daily Sales (In $1,000s) | Probability |
| 40 | 0.1 |
| 50 | 0.4 |
| 60 | 0.3 |
| 70 | 0.2 |
The probability of having sales of at least $50,000 is
| a. 0.5 |
| b. 0.90 |
| c. 0.10 |
| d. 0.30 |
51. Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.
| Production | |
| Per Month | Probability |
| 1 | 0.01 |
| 2 | 0.04 |
| 3 | 0.10 |
| 4 | 0.80 |
| 5 | 0.05 |
The expected monthly production level is
| a. 4.00 |
| b. 1.00 |
| c. 3.84 |
| d. 3.00 |
52. Which of the following is not a required condition for a discrete probability function?
| a. Σf(x) = 0 |
| b. Σf(x) = 1 |
| c. f(x) ≥ 0 for all values of x |
| d. All of these choices are correct. |
53. The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Which of the following discrete probability distributions’ properties are satisfied by random variable x?
| a. Poisson |
| b. Binomial |
| c. Hypergeometric |
| d. Normal |
54. The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.
| x | f(x) | |
| 0 | 0.80 | |
| 1 | 0.15 | |
| 2 | 0.04 | |
| 3 | 0.01 |
The mean and the standard deviation for the number of electrical outages (respectively) are
| a. 3 and 0.01 |
| b. 0.26 and 0.577 |
| c. 2.6 and 5.77 |
| d. 0 and 0.8 |
55. The expected value for a binomial distribution is given by equation
| a. np. |
| b. n(1 – p). |
| c. (n – 1)p. |
| d. (n – 1)(1 – p). |
56. Using a hypergeometric distribution with N = 6 and r = 2, what is the probability for n = 4 and x = 0?
| a. .9333 |
| b. .6667 |
| c. .0667 |
| d. .0001 |
57. The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The appropriate probability distribution for the random variable is
| a. continuous. |
| b. either discrete or continuous depending on how the interval is defined. |
| c. discrete. |
| d. binomial. |
58. The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is
| a. .9107 |
| b. .0241 |
| c. .0771 |
| d. .1126 |
59. Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.
| a. .5 |
| b. .025 |
| c. .05 |
| d. 0 |
60. The uniform distribution defined over the interval from 25 to 40 has the probability density function
| a. f(x) = 1/25 for 0 ≤ x ≤ 25 and f(x) = 1/40 for 26 ≤ x ≤ 40 |
| b. f(x) = 1/15 for 25≤ x ≤ 40 and f(x) = 0 elsewhere |
| c. f(x) = 5/8 for 25 ≤ x ≤ 40 and f(x) = 0 elsewhere |
| d. f(x) = 1/40 for all x |
61. The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA’s will have starting salaries of $34,000 to $46,000?
| a. 50% |
| b. 38.49% |
| c. 38.59% |
| d. 76.98% |
62. For a continuous random variable x, the height of the function at x is
| a. a value less than zero. |
| b. the probability at a given value of x. |
| c. 0.50, since it is the middle value. |
| d. named the probability density function f(x) |
63. A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
| a. 100.00 |
| b. 90.51 |
| c. 88.51 |
| d. 93.2 |
64. Suppose that the lifetime of batteries in a flashlight is exponentially distributed with a mean of 35 hours. What is the probability that the batteries will last between 25 and 30 hours?
| a. .4244 |
| b. .0651 |
| c. .5105 |
| d. .5756 |
65. Joe’s Record World has two stores and sales at each store follow a normal distribution. For store 1, μ = $2,000 and σ = $200 per day; for store 2, μ = $1,900 and σ = $300 per day. Which store is more likely to have a day’s sales in excess of $2200?
| a. Store 1 and store 2 are equally likely |
| b. Store 1 |
| c. Store 2 |
| d. More information is needed |
66. The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in less than 6 minutes is
| a. 1 |
| b. 0.15 |
| c. zero |
| d. 0.50 |
67. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing less than 250 pounds is
| a. 0.4772 |
| b. 0.5000 |
| c. 0.9772 |
| d. 0.0528 |
68. The probability density function for a uniform distribution ranging between 2 and 6 is
| a. any positive value. |
| b. undefined. |
| c. 4. |
| d. 0.25. |
69. For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is
| a. 0.0016 |
| b. 0.0160 |
| c. 0.1600 |
| d. 0.9452 |
70. Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.
| a. 30 |
| b. 235 |
| c. .03 |
| d. 75 |
71. The standard deviation of a normal distribution
| a. is always 0. |
| b. is always 1. |
| c. cannot be negative. |
| d. can be any value |
72. Which of the following distributions is not symmetric?
| a. Normal |
| b. Exponential |
| c. Standard normal |
| d. All of these choices are symmetric. |
73. A binomial probability distribution has p = 0.15 and n = 200. What is the probability of 20 to 25 successes?
| a. 0.17 |
| b. 0.08 |
| c. 0.10 |
| d. 0.95 |
74. z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803?
| a. -2.06 |
| b. -1.97 |
| c. 3.06 |
| d. 0.4803 |
75. Which of the following distributions is not symmetric?
| a. Normal |
| b. Exponential |
| c. Standard normal |
| d. All of these choices are symmetric. |
76. A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?
| a. 8.53% |
| b. 18.53% |
| c. 0.853% |
| d. 91.47% |
77. Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.
| a. 30 |
| b. 235 |
| c. .03 |
| d. 75 |
78. Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.
| a. 0 |
| b. .05 |
| c. .025 |
| d. .5 |
79. Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.
| a. 0 |
| b. .05 |
| c. .025 |
| d. .5 |
80. A small business owner determines that her revenue during the next year should be approximately normally distributed with a mean of $425,000 and a standard deviation of $130,000. What is the probability that her revenue will exceed $600,000?
| a. .9999 |
| b. .9115 |
| c. .5000 |
| d. .0885 |
81. The probability distribution that can be described by just one parameter is the
| a. binomial. |
| b. exponential. |
| c. uniform. |
| d. normal. |
82. A normal distribution with a mean of 0 and a standard deviation of 1 is called
| a. a probability density function. |
| b. a standard normal distribution. |
| c. exponential probability distribution. |
| d. uniform probability distribution. |
83. A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?
| a. 18.53% |
| b. 0.853% |
| c. 8.53% |
| d. 91.47% |
84. Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .9370?
| a. 1.50 |
| b. – 1.53 |
| c. 1.96 |
| d. .8264 |
85. Let x be a uniform random variable on the interval 1 ≤ x ≤ 6. What is the standard deviation of x?
| a. 2.08 |
| b. 1.44 |
| c. .2 |
| d. 3.5 |
86. For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is
| a. 0.1600 |
| b. 0.0016 |
| c. 0.9452 |
| d. 0.0160 |
87. For a uniform probability density function,
| a. the height of the function is the same for each value of x. |
| b. the height of the function cannot be larger than one. |
| c. the height of the function is different for various values of x. |
| d. the height of the function decreases as x increases. |
88. Which of the following is not a characteristic of the normal probability distribution?
| a. The mean of the distribution can be negative, zero, or positive |
| b. The standard deviation must be 1 |
| c. The mean, median, and the mode are equal |
| d. The distribution is symmetrica |
89. What is the mean of x, given the function below?
f(x) =(1/10) e-x/10x ≥ 0
| a. 100 |
| b. 0.10 |
| c. 10 |
| d. 1,000 |
90. For the standard normal probability distribution, the area to the right of the mean is
| a. 1.96. |
| b. 3.09. |
| c. 1. |
| d. 0.5. |
91. A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is
| a. different for each interval. |
| b. zero. |
| c. the same for each interval. |
| d. at least one. |
92. Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.5?
| a. 1.0000 |
| b. 0.1915 |
| c. 0.3413 |
| d. 0.0000 |
93. The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?
| a. 50% |
| b. 1.96% |
| c. 21% |
| d. It could be any value, depending on the magnitude of the standard deviation |
94. z is a standard normal random variable. The P(1.05 ≤ z ≤ 2.13) equals
| a. 0.4834 |
| b. 0.3531 |
| c. 0.8365 |
| d. 0.1303 |
95. A value of 0.5 that is added to and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called
| a. factor of conversion. |
| b. probability density factor. |
| c. continuity approximation factor. |
| d. continuity correction factor. |
96. For a normal distribution, a negative value of z indicates
| a. the area corresponding to the z is negative. |
| b. the z is to the left of the mean. |
| c. the z is to the right of the mean. |
| d. a mistake has been made in computations, because z is always positive |
97. Let F be the event that a customer is dissatisfied with the food at a restaurant and let S be the event that a customer is dissatisfied with the service. If P(F) = .15, P(S) = .40, and P(F ∩ S) = .10, what is the probability that a customer is dissatisfied with either the service or the food?
| a. .55 |
| b. .45 |
| c. .65 |
| d. .10 |
98. The collection of all possible sample points in an experiment is
| a. a combination. |
| b. the sample space. |
| c. the population. |
| d. an event. |
99. If A and B are independent events with P(A) = .1 and P(B) = .4, then
| a. P(A ∩ B) = .04. |
| b. P(A ∩ B) = .25. |
| c. P(A ∪ B) = .5. |
| d. P(A ∩ B) = 0 |
100. If P(A) = 0.75, P(A ∪ B) = 0.86, and P(A ∩ B) = 0.56, then P(B) =
| a. 0.67. |
| b. 0.56. |
| c. 0.25. |
| d. 0.11. |
101. Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?
| a. 64 |
| b. 4 |
| c. 32 |
| d. 16 |
102. The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the
| a. counting rule for multiple-step experiments. |
| b. counting rule for combinations. |
| c. counting rule for independent events. |
| d. counting rule for permutations. |
103. The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the
| a. counting rule for multiple-step experiments. |
| b. counting rule for combinations. |
| c. counting rule for independent events. |
| d. counting rule for permutations |
104. In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the
| a. Binomial distribution. |
| b. Poisson distribution. |
| c. Normal distribution. |
| d. Uniform distribution |
105. Random variable x has the probability function: f(x) = x/6 for x = 1,2 or 3. The expected value of x is
| a. 2.333 |
| b. 0.500 |
| c. 0.333 |
| d. 2.000 |
106. Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.
| Production | |
| Per Month | Probability |
| 1 | 0.01 |
| 2 | 0.04 |
| 3 | 0.10 |
| 4 | 0.80 |
| 5 | 0.05 |
The expected monthly production level is
| a. 4.00 |
| b. 3.00 |
| c. 1.00 |
| d. 3.84 |
107. Which of the following is not a required condition for a discrete probability function?
| a. Σf(x) = 0 |
| b. Σf(x) = 1 |
| c. f(x) ≥ 0 for all values of x |
| d. All of these choices are correct |
108. The mean of a standard normal probability distribution
| a. can be any value as long as it is positive. |
| b. can be any value. |
| c. is always equal to zero. |
| d. is always greater than zero |
109. The probability density function for a uniform distribution ranging between 2 and 6 is
| a. 4. |
| b. undefined. |
| c. any positive value. |
| d. 0.25. |
110. The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?
| a. 0.4772 |
| b. 0.0228 |
| c. 0.9772 |
| d. 0.5000 |
111. Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.
| a. 30 |
| b. .03 |
| c. 235 |
| d. 75 |
112. A standard normal distribution is a normal distribution with
| a. any mean and a standard deviation of 1. |
| b. a mean of 0 and standard deviation of 1. |
| c. a mean of 0 and a standard deviation of 0. |
| d. a mean of 1 and a standard deviation of 1. |
113. Posterior probabilities are computed using
| a. Chebyshev’s theorem. |
| b. the empirical rule. |
| c. relative frequency. |
| d. Bayes’ theorem. |
114. A graphical method of representing the sample points of an experiment is a
| a. dot plot. |
| b. stem-and-leaf display. |
| c. stacked bar chart. |
| d. tree diagram. |
115. Which of the following statements is always true?
| a. P(A) + P(B) = 1 |
| b. ∑P ≥ 1 |
| c. -1 ≤ P(Ei) <≤ 1 |
| d. P(A) = 1 – P(Ac) |
116. Events that have no sample points in common are
| a. complements. |
| b. posterior events. |
| c. independent events. |
| d. mutually exclusive events. |
117. If a coin is tossed three times, the likelihood of obtaining three heads in a row is
| a. 0.500. |
| b. 0.875. |
| c. 0.125. |
| d. 0.0. |
118. If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are
| a. complements of each other. |
| b. independent events. |
| c. non-mutually exclusive. |
| d. mutually exclusive. |
119. If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is
| a. 0. |
| b. larger than the probability of tails. |
| c. 1/2. |
| d. 1/16 |
120. The intersection of two mutually exclusive events
| a. can be any value between 0 to1. |
| b. must always be equal to 1. |
| c. can be any positive value. |
| d. must always be equal to 0. |
121. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The intersection of A and B is
| a. all accounts fewer than 31 or more than 60 days past due. |
| b. all accounts from new customers and all accounts that are from 31 to 60 days past due. |
| c. all new customers. |
| d. all new customers whose accounts are between 31 and 60 days past due. |
122. Initial estimates of the probabilities of events are known as
| a. posterior probabilities. |
| b. conditional probabilities. |
| c. prior probabilities. |
| d. subjective probabilities |
123. An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is
| a. 0.100. |
| b. 0.024. |
| c. 0.900. |
| d. 0.500. |
124. When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the
| a. subjective method. |
| b. posterior method. |
| c. classical method. |
| d. relative frequency method. |
125. If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are
| a. mutually exclusive. |
| b. non-mutually exclusive. |
| c. complements of each other. |
| d. independent events. |
126. An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is
| a. 8. |
| b. 2. |
| c. 4. |
| d. 16. |
127. If P(A) = 0.50, P(B) = 0.40 and P(A ∪ B) = 0.88, then P(B |A) =
| a. 0.03. |
| b. 0.02. |
| c. 0.04. |
| d. 0.05 |
128. The prior probabilities for events A1 and A2 are P(A1) = .25 and P(A2) = .75. The conditional probabilities of event B given A1 and A2 are P(B | A1) = .45, and P(B | A2) = .30. Using Bayes’ theorem, what is the posterior probability P(A2 | B)?
| a. .667 |
| b. .775 |
| c. .225 |
| d. .338 |
129. Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)
| a. 16 |
| b. 2 |
| c. 4 |
| d. 12 |
130. The union of events A and B is the event containing all the sample points belonging to
| a. A or B or both. |
| b. B or A. |
| c. A or B, but not both. |
| d. A or B. |
131. A six-sided die is tossed 3 times. The probability of observing three ones in a row is
| a. 1/6. |
| b. 1/216. |
| c. 3/6. |
| d. 1/27. |
132. If A and B are independent events with P(A) = .1 and P(B) = .4, then
| a. P(A ∩ B) = .25. |
| b. P(A ∩ B) = .04. |
| c. P(A ∪ B) = .5. |
| d. P(A ∩ B) = 0. |
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