# mqm406_multiplechoice_chapter7

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PROBABILITY DISTRIBUTIONS -- DISCRETE: CHAPTER 7 1. Number of accidents that occur annually on a busy intersection is an example of: a. continuous random variable b. discrete random variable c. discrete probability distribution d. continuous probability distribution 2. A random variable is a variable whose value is determined by: a. the outcome of an experiment and associated with probability b. the random population c. the random space d. all of the above 3. A discrete random variable is a random variable: a. that can assume any value in one or more intervals b. whose values are countable c. that is derived from a random population d. that is determined by random probability 4. A table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities is called a: a. probability distribution b. random variable c. bivariate distribution d. probability tree 5. A continuous random variable is a random variable: a. that can assume any value in one or more intervals b. whose values are countable c. that is derived from a random population d. that is determined by random probability 6. Which of the following is not an example of a discrete random variable? a. The number of days it rains in a month in New York b. The number of stocks a person owns c. The number of persons allergic to penicillin d. The time spent by a physician with a patient 7. Which of the following is an example of a discrete random variable? a. The weight of a box of cookies b. The length of a window frame c. The number of horses owned by a farmer d. The distance from home to work for a worker

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8. The probability distribution table of a discrete random variable lists: a. some of the values that the random variable can assume and their corresponding probabilities b. all the values that the random variable can assume and their corresponding probabilities c. all the values that the random variable can assume and their corresponding frequencies d. all of these 9. If X and Y are random variables, the sum of all the conditional probabilities of X given a specific value of Y will always be: a. 0.0 b. 1.0 c. the average of the possible values of X d. a value larger than zero but smaller than 1.0 10. For a discrete random variable x, the probability of any value of x is: a. always greater than 1 b. always less than zero c. always in the range zero to 1 d. never greater than zero 11. Which of the following is true for the probability of a discrete random variable x? a. p(x) < 0 b. p(x) > 1 c. p(x) = 2 d. 0 P(x) 11 12. For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be: a. equal to zero b. in the range zero to 1 c. equal to .5 d. equal to 1 13. Which of the following is true for the probability distribution of a discrete random variable x? a. P(x) < 0 b. P (x) = 1 c. P (x) = 2 d. P (x) > 1 Following table lists the probability distribution of a discrete random variable x (number of cars) for families in Bloomington.

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x 0 1 2 3 4 5 6 7

P(x) .04 .11 .18 .24 .14 .17 .09 .03

14. The probability of x = 3 is: a. .57 b. .24 c. .43 d. .18 15. The probability that x is less than 5 is: a. .71 b. .88 c. .14 d. .17 16. The probability that x is greater than 3 is: a. .67 b. .24 c. .57 d. .43 17. The probability that x is less than or equal to 5 is: a. .88 b. .71 c. .12 d. .29 18. The probability that x is greater than or equal to 4 is: a. .29 b. .14 c. .43 d. .57 19. The probability that x assumes a value from 2 to 5 is: a. .17 b. .73 c. .38 d. .12

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20. If X and Y are random variables with V(X) = 7.5, V(Y) = 6 , then V(2X+3Y) is: a. 33 b. 37 c. 84 d. 132 Following table lists the probability distribution of the number of computers owned by all families in a city. x P(x) 0 .02 1 .65 2 .26 3 .07 21. The probability that a randomly selected family owns exactly two computers is: a. .07 b. .93 c. .26 d. .33 22. The probability that a randomly selected family owns at most one computer is: a. .65 b. .67 c. .98 d. .33 23. The probability that a randomly selected family owns at least two computers is: a. .33 b. .26 c. .93 d. .67 24. The probability that a randomly selected family owns less than two computers is: a. .93 b. .33 c. .26 d. .67 25. The probability that a randomly selected family owns more than one computer is: a. .65 b. .33 c. .98 d. .67 26. If X and Y are random variables with E(X) = 5 and E(Y) = 8, then E(2X+3Y) is: a. 34

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b. 13 c. 18 d. 40 27. The mean of a discrete random variable is the mean of its a. frequency distribution b. percentage distribution c. probability distribution d. all of these 28. The mean of a discrete random variable is also called its: a. box-and-whisker measure b. expected value c. second quartile d. upper hinge 29. The mean of a discrete random variable is obtained by using the formula: a. (x )P(x) b. yP(x) c. m d. xP(x) 30. If X and Y are any random variables, which of the following identities is not true? a. E(X+Y) = E(X) + E(Y) b. E(X-Y) = E(X) - E(Y) c. V(X+Y) = V(X) + V(Y) d. V(X-Y) = V(X) - V(Y) 31. The standard deviation of a discrete random variable is the standard deviation of its: a. frequency distribution b. percentage distribution c. probability distribution d. all of these The following table lists the probability distribution of a discrete random variable x (number of children) of a family in a small city. x P(x) 0 .04 1 .11 2 .18 3 .24 4 .14 5 .17 6 .09 7 .03

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32. The mean of the random variable x is: a. 3.70 b. 5.47 c. 3.35 d. 1.89 33. The standard deviation of the random variable x is approximately: a. 2.97 b. 14.19 c. 6.91 d. 1.72 34. If X and Y are independent random variables, which of the following identities is always true? a. E(2X+3Y) = E(X) + E(Y) b. V(2X+3Y) = 2 V(X) + 3 V(Y) c. V(2X+3Y) = 4 V(X) + 5 V(Y) d. E(2X+3Y) = 2 E(X) + 3 E(Y) The following table lists the probability distribution of the number of TV sets owned by all families in a city. X P(x) 0 .07 1 .38 2 .31 3 .16 4 .08 35. The mean number of TV sets owned by these families is: a. 4.34 b. 1.80 c. 2.08 d. 3.25 36. The standard deviation of the number of TV sets owned by these families is approximately: a. 4.34 b. 2.08 c. 1.80 d. 1.05 37. In general, "n factorial" represents: a. the product of any n numbers b. the sum of all integers from n to 1 c. the product of all integers from n to 1 d. n 1 6

38. The factorial of zero is: a. zero b. 1 c. 10 d. cannot be determined 39. The factorial of 8 is: a. 36 b. 40,320 c. 5040 d. 35 40. The factorial of (14 8) is: a. 720 b. 21 c. 120 d. 20 41. The factorial of (8 8) is: a. zero b. 362,880 c. 1 d. 81 42. The factorial of (4 0) is: a. 24 b. 1 c. zero d. 10 43. Which of the following is not a characteristic of a binomial experiment? a. There is a sequence of identical trials b. Each trial results in two or more outcomes. c. The trials are independent of each other. d. Probability of success p is the same from one trial to another. 44. The number of combinations for selecting 7 elements from 10 distinct elements is: a. 70 b. 120 c. 3 d. 100 45. The number of combinations for selecting zero elements from 7 distinct elements is: a. 1

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b. 5040 c. 7 d. zero 46. The number of combinations for selecting 9 elements from 9 distinct elements is: a. zero b. 1 c. 81 d. 362,880 47. A jury of five persons will be randomly selected from a group of 15 persons. The total number of combinations are: a. 3,628,800 b. 5005 c. 3003 d. 120 48. An investor will randomly select six stocks from 18 stocks for an investment purpose. The total number of combinations are: a. 18,564 b. 479,001,600 c. 720 d. 8,568 49. A Bernoulli trial is: a. the trial of a court case b. a repetition of a binomial experiment c. a repetition of a probability distribution d. the trial of a probability distribution 50. Which of the following is not a condition of the binomial experiment? a. There are only two trials. b. Each trial has two and only two outcomes. c. p is the probability of success, q is the probability of failure, and p + q = 1. d. The trials are independent. 51. In binomial experiments, the outcome called a "success" is an outcome: a. that is always beneficial b. that is linked to success c. to which the question refers d. that is favorable 52. The expected value of a binomial probability distribution is: a. n + p b. npq c. np

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d. n + p + q 53. The parameters of the binomial probability distribution are: a. n, p, and q b. n, p, q, and x c. n, p, and x d. n and p 54. The binomial probability distribution is symmetric if: a. p is equal to .25 b. p is equal to .50 c. p is less than .50 d. p is greater than .50 55. The binomial probability distribution is skewed to the right if: a. p is .25 or smaller b. p is .50 c. p is less than .50 d. p is greater than .50 56. The binomial probability distribution is skewed to the left if: a. p is .25 or greater b. p is equal to .50 c. p is less than .50 d. p is greater than .50 57. The mean of a binomial distribution is: a. npq b. np c. square of npq d. square root of npq 58. The standard deviation of a binomial distribution is: a. npq b. np c. square of npq d. square root of npq 59. Which of the following is an example of a binomial experiment? a. Rolling a die 10 times and observing for a number b. Selecting five persons and observing whether they are in favor of an issue, against it, or have no opinion c. Tossing a coin 20 times and observing for a head or a tail d. Drawing three marbles from a box that contains red, blue, and yellow marbles 60. Which of the following is not an example of a binomial experiment?

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a. Rolling a die 25 times and observing for an even or an odd number b. Selecting 50 items from the production line and observing if they are good or defective c. Rolling a die 20 times and observing f