8. Assume that blood types are distributed in the population as follows: type A, 30%; type B, 20%; type AB, 15%; and type O, 35%. A blood bank needs 5 type O donors. Let X be the number of persons needed to be tested to find exactly 5 type O donors. (a) What is the p.m.f. of X? (b) Find the probability that 8 people need to be tested to find 5 type O donors. (c) What is the expected number of people needed to be tested to find 5 type O donors? (d) What is the probability that fewer than 20 people need to be tested to find exactly 1 type AB donor? The number of death claims processed per month by an insurance company is a Poisson random variable, X, with a mean of 5.2. (a) Find P( 3