In the following situations identify the appropriate probability distribution. Give its parameters. Use the user-defined functions of the Random Variables Add-in to answer the numerical questions.

a. A department at the University has twenty professors. Ten are full professors, four are associate professors and six are assistant professors. The chairman selects four names at random from the faculty to form a committee. What is the probability at least three members of the committee are full professors?

b. You have the job of hiring three workers to accomplish some task. Twenty candidates are waiting for interviews. You will interview each candidate in turn, and if he or she is acceptable you will hire the person immediately. The probability that a candidate is acceptable is 0.6. What is the probability that you will fill the three positions with ten or fewer interviews?

c. A major company needs three engineers but will accept more. The manager in charge of hiring will conduct ten interviews in hopes of finding at least three “good” applicants who will accept the offer of a job. The probability that an applicant is “good” is 0.4, and the probability that a “good” applicant will accept the job is 0.6. She makes offers to every “good” applicant. We assume applicants are independent. What distribution describes the number of engineers she will hire? What is the probability that at least three will be hired?

d. A robot insertion tool must place 4 rivets on a printed circuit board. Rivets are presented to it at random, but 10% of the rivets are faulty. When a faulty rivet is encountered it must be discarded, and another drawn. We want to compute probabilities regarding the number of draws required before 4 good rivets are found. In particular what is the probability that exactly 10 draws are required before we find 4 good rivets.