A lot is known to be 1.2% defective. Five units are randomly selected from the lot, and the lot is accepted if 1 or fewer defects are found. What is the probability of the lot being rejected?

Question

Quizplus · Accepted Answer

To find the probability of the lot being rejected, we need to find the probability of finding 2 or more defects in a sample of 5 units. This can be calculated using the binomial distribution as follows:
P(2 or more defects) = 1 - P(0 or 1 defect)
P(0 or 1 defect) = P(0 defects) + P(1 defect)
P(0 defects) = (0.988)^5 = 0.939
P(1 defect) = 5C1 * (0.012) * (0.988)^4 = 0.052
P(0 or 1 defect) = 0.939 + 0.052 = 0.991
P(2 or more defects) = 1 - 0.991 = 0.009
Therefore, the probability of the lot being rejected is 0.009 or 0.173%. The closest answer choice is C, 0.00173.

A Lot Is Known to Be 1