Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, highpitched, oscillating 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. (a) Calculate P(x 4) and P(X s P(X=4) = 0.4196 P(X 4) 10.8012 4). (Round your answers to four decimal places.)
(b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) 0.9207 Enter a number
(c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 10 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X 2) than to use the hypergeometric pmf. distribution if the population size We can approximate the hypergeometric distribution with the -Select and the number of successes are large. Here n = and p = M/N= Approximate P(X 2) using that method. (Round your answer to three decimal places.)