Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 7 of these refrigerators have a defective compressor and the other 4 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 -5) and P(X S 5). (Round your answers to four decimal places.)
P(X = 5) =
(b) Determine the probability that χ exceeds its mean value by more than 1 standard deviation. Round your answer to four decimal places.
(c) Consider a large shipment of 500 refrigerators, of which 50 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 S 2) than to use the hypergeometric pmf distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the binomial n= and p = M/N = Approximate P(X S 2) using that method. (Round your answer to three decimal places.) P(X 2) 0.8183 X