Cappelli Inc. designs and manufactures women's apparel using material from various mills. Their acceptance sampling plan states that 20 two-inch squares of the incoming material must be carefully checked. If 3 or less squares reveal imperfections,the lot is accepted. What is the probability that an incoming lot from Blufton Mills that contains 40 percent imperfect cloth will be accepted?
A)0
B)0.239
C)0.016
D)0.0024

Question

Quizplus · Accepted Answer

Since the lot contains 40% imperfect cloth, the probability of a square being imperfect is 0.4.

Thus, the number of squares out of 20 that will be imperfect follows a binomial distribution with n=20 and p=0.4.

The probability of 3 or less squares revealing imperfections is given by the cumulative probability of the binomial distribution:

P(X ≤ 3) = Σ P(X = k), k= 0, 1, 2, 3

Using a binomial calculator or table, we find:

P(X ≤ 3) = 0.016

Therefore, the probability that an incoming lot from Blufton Mills will be accepted is 0.016 or 1.6%. Hence, the best choice is (C).