Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscil- lating noise when the refrigerators are running. Suppose that 7 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. Compute the following:

a. P(X = 5)

b. P(X 4)

c. The probability that X exceeds its mean value by more than I standard deviation.

d. Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 15 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X 5) than to use the hypergeo- metric pmf.