A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
A)0.0004
B)0.0038
C)0.10
D)0.02

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the sample size, k is the number of defective parts in the sample, p is the probability of a part being defective, and (n choose k) is the binomial coefficient.

In this case, n=5, k=2, p=0.02, and (n choose k) = 5 choose 2 = 10.

Plugging these values into the formula, we get:
P(X=2) = 10 * (0.02)^2 * (0.98)^3 = 0.0038

Therefore, the answer is B.

A Production Process Produces 2% Defective Parts