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2 out of every 20 parts produced by a machine are defective. For quality control, 15 products are checked and the defective ones are discarded. Using hypergeometric distribution, calculate the probability of the lot being rejected.

Answer :

Final answer:

To calculate the probability of the lot being rejected using the hypergeometric distribution, we need to use the formula P(X=x) = (C(K, x) * C(N-K, n-x)) / C(N, n). In this case, the probability is approximately 0.399.

Explanation:

To calculate the probability of the lot being rejected using the hypergeometric distribution, we need to use the formula P(X=x) = (C(K, x) * C(N-K, n-x)) / C(N, n), where N is the population size, K is the number of defective parts in the population, n is the sample size, and x is the number of defective parts in the sample.

In this case, N = 20, K = 2, n = 15, and we want to find the probability that x is greater than or equal to 1, since even a single defective part will lead to the lot being rejected.

Using the formula and performing the calculations, the probability of the lot being rejected is approximately 0.399.

Learn more about Hypergeometric distribution here:

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