Question

Suppose a lot of 10,000 items has 200 defective items and that a random sample of 30 is drawn from the lot. What is the Poisson approximation (to four decimal places) of the probability of getting exactly 3 defective in the sample?

Answer 1

Solution: We are given a lot of 10,000 items have 200 defectives.

Therefore, the proportion of defective items is:

Now, we can find the average number of defective for a random sample of 30 items as:

We are required to find the probability of getting exactly 3 defective in the sample.

Let x be the number of defectives in a sample.

Therefore, we have to find:

Now using the Poisson approximation, we have:

Therefore, the Poisson approximation of the probability of getting exactly 3 defective in the sample is 0.0198