Question

A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less, the lot passes inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection

Answer 1

0.1979 or 19.79%

Explanation:

If 20% of all bulbs are defective, there is a 20% chance of each bulb being defective and an 80% chance of each bulb not being defective.

This is a binomial probability model with probability of success (bulb being defective) of p=0.20.

In order for the lot to pass inspection, it must contain either zero or one defective bulb, the probability of one of these scenarios occurring is:

`Pass= P(d=0)+P(d=1)\\Pass= 0.80^(14)+14*0.20*0.80^(13)\\Pass=0.1979`

The probability that the lot will pass inspection is 0.1979 or 19.79%.