(c) Consider a large shipment of 400 refrigerators, of which 40 have defective c

Question

(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 s 5) than to use the hypergeometric pmf We can approximate the hypergeometric distribution with the binomial n=25 distribution if the population size and the number of successes are large. Here and p = MIN = .1 Approximate P(X 5) using that method. (Round your answer to three decimal places.)

Explanation / Answer

The hypergeometric distribution formula is as shown below: -

h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]

where N=400, k=40, n=25 and x would be 0,1,2,3,4 and 5 and using the above formula for hypergeometric distribution, we get the answer to be 0.9713.

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