A lot of 25 skylight covers are received at your construction site, and before installation are subjected to an acceptance testing procedure. The procedure consists of selecting 5 covers at random, without replacement, and testing each one using projectile to simulate hail stone impacts. If 2 or fewer of the 5 covers crack, the remaining ones are accepted. Otherwise the lot is rejected and sent back to the supplier. Assume a lot actually has four defective covers (impact strength is not adequate to withstand the test) among the 25. What is the exact probability of lot acceptance? Hint: Hypergeometric.

If the lot has 4 defective covers out of 25 total covers, the probability of accepting the lot is P=0.98.

Step-by-step explanation:

We have a population of N=25 skylight covers, were K=4 are defective.

We sample n=5 covers, and we will accept the lot if k=2 or fewer are defective.

We will use the hypergeometric distribution to model this probabilities.

First, to be accepted, the sample can have 2, 1 or 0 defective covers, so the probability of being accepted is:

The probability that there are k defective covers in the sample is:

Then, we can calculate the individual probabilities as:

If we add this probabilities, we have:

If the lot has 4 defective covers out of 25 total covers, the probability of accepting the lot is P=0.98.