Say that we will perform a single sampling plan of (40,2) in an incoming batch of 1000 units. That is, we will randomly pick 40 units, inspect each, and if 2 or fewer are defective, we will accept the batch; else we will reject the batch.

If the incoming batch had 8 defective items in it, what is the probability of accepting the batch?

Here we can assume a binomial distribution B of defective items in the sample with n = 40, p = 0.008. So P(acceptance) = P(B <= 2) = "binom.dist(2, 40, 0.008, true)" (in Excel)

(Provide three decimal places)

Number of defects per unit was recorded for a sample of ten items in a production line, and they were:

1, 1, 0, 1, 1, 1, 0, 1, 1, and 0

What is the average number of defects per unit from the above sample?