Each of11refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that8of these refrigerators have a defective compressor and the other3have less serious problems. If the refrigerators are examined in random order, letXbe the number among the first7examined that have a defective compressor.

(a) CalculateP(X=5) andP(X5).

(b) Determine the probability thatXexceeds its mean value by more than 1 standard deviation.

(c) Consider a large shipment of500refrigerators, of which50have defective compressors. IfXis the number among20randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)P(X2)

than to use the hypergeometric pmf.

We can approximate the hypergeometric distribution with the binomial distribution if the population size and the number of successes are large.What is n and p=M/N?

(d) ApproximateP(X2) using that method.