probability

Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigeratoris running. Suppose that 7 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are exam- ined in random order, let X be the number among the rst 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 1 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 re- frigerators that have defective compressors, de- scribe a less tedious way to calculate (at least approximately) P(X <>5) than to use the hyper- geometric pmf.