In a batch of 100 cell phones, there are, on average, 6 defective ones. If a random sample of 25 is selected, find the probability of 3 defective ones.
A) 0.0600
B) 0.2500
C) 0.1200
D) 0.1303

Question

Quizplus · Accepted Answer

This problem can be solved using the hypergeometric distribution formula, which is appropriate for sampling without replacement from a finite population. The probability of getting exactly k defective items in a sample of size n from a population of size N with K defective items is given by the formula: P(X = k) = [C(K, k) * C(N-K, n-k)] / C(N, n), where C(n, k) is the combination of n items taken k at a time. Plugging in the values: P(3 defective) = [C(6, 3) * C(94, 22)] / C(100, 25), calculating this gives a probability of approximately 0.1303.

In a Batch of 100 Cell Phones, There Are, on Average