Question

Each of 13 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 10 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 8 examined that have a defective compressor.

(a) Calculate P(X = 6) and P(X ≤ 6). (Round your answers to four decimal places.)

P(X = 6) =

P(X ≤ 6) =

(b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)

(c) Consider a large shipment of 600 refrigerators, of which 60 have defective compressors. If X is the number among 20 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 4) 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. Here n = 20 and p = M/N = 0.1.

Approximate P(X ≤ 4) using that method. (Round your answer to three decimal places.)

P(X ≤ 4) ≈

Answer 1