An interviewer is given a list of potential people she can interview. Suppose th

Question

An interviewer is given a list of potential people she can interview. Suppose that the interviewer needs to interview five people and that each person independently agrees to be interviewed with probability 0.6. Let X be the number of people she must ask to be interviewed to obtain her necessary number of interviews.

a What is the probability that she will be able to obtain the five people by asking no more than seven people?

b What is the expected value and variance of the number of people she must ask to interview five people?

Please show your detailed work!! Thank you.

Explanation / Answer

a. This is an instance of binomail probability. Use the following formula to obtain the required probbaility.

P(x,r)=nCr(p)^r(q)^n-r, where p denotes the probability of success, n is the number of trials, and r is thespecific number of events to have occured.

P(x=5)=7C5(0.6)^5(0.4)^2=0.261

b. E(5X)=5np=5*7*0.6=21; SD(5X)=sqrt Var(5X)=sqrt 25 Var(X)=sqrt 25 npq= sqrt 25 7*0.6*0.4=6.48

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