Blood type A occurs in about 41% of the population (Reference: Laboratory and Diagnostic Tests by F. Fischbach). A clinic needs 3 pints of type A blood. A donor usually gives a pint of blood. Let n be a random variable representing the number of donors needed to provide 3 pints of type A blood.

(a) Explain why a negative binomial distribution is appropriate for the random variable n. Write out the formula for P(n) in the context of this application.

(b) Compute P(n = 3), P(n = 4), P(n = 5), and P(n = 6).

(c) What is the probability that the clinic will need from three to six donors to obtain the needed 3 pints of type A blood?

(d) What is the probability that the clinic will need more than six donors to obtain 3 pints of type A blood?

(e) What are the expected value m and standard deviation s of the random variable n? Interpret these values in the context of this application.