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 8 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 ≤ 4).

(Round your answers to four decimal places.)

P(X = 4)

=

P(X ≤ 4)

=

(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 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)

P(X ≤ 7)

than to use the hypergeometric pmf.We can approximate the hypergeometric distribution with the  ---Select--- binomial geometric negative binomial distribution if the population size and the number of successes are large. Here

n =

and

p = M/N =  .

Approximate

P(X ≤ 7)

using that method. (Round your answer to three decimal places.)

P(X ≤ 7)

≈

Answer 1