Under which of the following conditions would it be appropri

Under which of the following conditions would it be appropriate to use a Binomial random variable? In each case, explain why your answer is correct.

A. A department will interview 10 candidates for a position, and call back for a second interview those who answer the interview questions to the satisfaction of all the interviewers. They hope to call back at least 3, but past experience suggests an average of about 1 call back per 4 interviews.

B. A factory posts on the wall the number of days since its last safety infraction or injury. in the past year, the factory has had a safety infraction or injury on 6 different days. The factory is interested in the number of days that can be expected to elapse without an injury.

C. Fifteen of a doctor\'s patients have th same ailment. Studies have shown that about 86.5% of patients with this ailment respond to a certain drug. The doctor prescribes the drug to all 15, but the number who will respond in this case is, of course, not known in advance.

Solution

A) Assuming all interviews of all 10 candidates are independent, given probability of successful interview is 1/4, The number of candidates called for second itnerview is binomial random variable with with n=10, p = 1/4

B) Number of days without injury has no upper bound, and thus this is not a binomial random variable, instead it seems to be poisson random variable.

C) NUmber of patients responding to drug is binomial random variable because: all 15 patients are independent, each patient either responds (success) or does not respond (failure), where probability of succes in each trial is constant, i.e, 0.865.