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) 0.015
D) 0.0024

Question

Quizplus · Accepted Answer

The probability of a square being imperfect is 0.4 since 40% of the cloth is imperfect. The number of squares that can be imperfect and still have the lot accepted is 3 or less. We can use the binomial distribution to calculate the probability of having 3 or fewer imperfect squares out of 20 total squares.

P(X <= 3) = Σ(i=0 to 3) (20 choose i) * (0.4)^i * (0.6)^(20-i)

P(X <= 3) = 0.015

Therefore, the probability of an incoming lot from Blufton Mills that contains 40% imperfect cloth being accepted is 0.015.