Suppose a job seeker is invited to interview for a particular job, the job seeke

Question

Suppose a job seeker is invited to interview for a particular job, the job seeker is either offered a job or not. If selected for the job, the job seeker can choose to accept the offer or reject. Suppose an employer has offered jobs to 500 applicants, but only has a budget for 375 of them. Let the applicants who were offered jobs be independent of one another, and the chance that a given job seeker will accept the offer be 0.75. a. What is the probability that the employer will have the budget for all job applicants that accept their offer? b. Now say we go down the list of job applicants that the employer gave offers to (the list of 500). Starting with the first name, and going in order (1 to 500), let X be the number of names (job applicants) you go through before you reach the first one that accepts the offer. What distribution does X follow, and what is the parameter?

Explanation / Answer

a. Total applicants = 500; budget is only to hire 375 among them

Pr(One accept the offer) = 0.75

so Expected number of people who accpt the offer = 500 * 0.75 = 375

so probability that the employer will have the budget for all job aplicants that accept their offer when there are less than 375 applicants accept the offer.

Pr(X<= 375) = it will be a binomial distribution but very impossible to calculate so we will use Poisson approximation or normal approximation

by Poisson approximation Pr(X<= 375) = e- ()x/x! = 0.5171 [ where = 375]

by normal approximation Pr(X<= 375) = 0.50

(b) In the given question, the distribution it follows is the Geometric distribution.

Pr (X=x) = (1-p)k-1 (p) where p = 0.75

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