Random Variable and Binomial Setting
8.1 BINOMIAL SETTING? In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case.
(a) An auto manufacturer chooses one car from each hour’s production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc.) in the car’s paint. No: There is no fixed n (i.e., there is no definite upper limit on the number of defects).
(b) The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty; X is the number who say “Yes.” Yes
B: Only two choices, yes or no
I: It is reasonable to believe that all responses are independent (ignoring any “peer pressure”)
N: n = 100
S: All have the same probability of saying “yes” since they are randomly chosen from the population (c) Joe buys a ticket in his state’s “Pick 3” lottery game every week; X is the number of times in a year that he wins a prize. Yes
B: Only two choices, win or lose
I: All responses are independent
N: n = 52
S: In a “Pick 3” game, Joe’s chance of winning the lottery is the same every week
8.2 BINOMIAL SETTING? In each of the following cases, decided whether or not a binomial distribution is an appropriate model, and give your reasons.
(a) Fifty students are taught about binomial distributions by a television program. After completing their study, all students take the same examination. The number of students who pass is counted. YES
B:
http://www.lz95.org/assets/1/6/Ch8_HW_Kirkwood_Solutions.pdf
. [15 points] How many calls? Calls to the customer service department of a cable TV provider are made randomly and independently at a rate of 11 per minute. The company has a staff of 20 customer service specialists who handle all the calls. Assume that none of the specialists are on a call at this moment and that a
(a) An auto manufacturer chooses one car from each hour’s production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc.) in the car’s paint. No: There is no fixed n (i.e., there is no definite upper limit on the number of defects).
(b) The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty; X is the number who say “Yes.” Yes
B: Only two choices, yes or no
I: It is reasonable to believe that all responses are independent (ignoring any “peer pressure”)
N: n = 100
S: All have the same probability of saying “yes” since they are randomly chosen from the population (c) Joe buys a ticket in his state’s “Pick 3” lottery game every week; X is the number of times in a year that he wins a prize. Yes
B: Only two choices, win or lose
I: All responses are independent
N: n = 52
S: In a “Pick 3” game, Joe’s chance of winning the lottery is the same every week
8.2 BINOMIAL SETTING? In each of the following cases, decided whether or not a binomial distribution is an appropriate model, and give your reasons.
(a) Fifty students are taught about binomial distributions by a television program. After completing their study, all students take the same examination. The number of students who pass is counted. YES
B:
http://www.lz95.org/assets/1/6/Ch8_HW_Kirkwood_Solutions.pdf
. [15 points] How many calls? Calls to the customer service department of a cable TV provider are made randomly and independently at a rate of 11 per minute. The company has a staff of 20 customer service specialists who handle all the calls. Assume that none of the specialists are on a call at this moment and that a