[mouse26]

Hi everyone. So this question came up in my class, and I am trying to figure out the answer, but I am not so sure where to start. I was wondering if anyone knew the answer and if they do could they give me the full solution. Thanks a lot!

Suppose in a container at a factory, there are 1000 parts. It is known that 40 of the parts are
defective. We pull out 25 parts without replacement, and see how many are defective. We are
interested in the number of defectives. The number of defectives in our sample of 25 does not follow a binomial distribution exactly, since the probability of getting a defective part changes from trial to trial. For example, for the first part selected the probability it is defective is 40/1000 = .04, but if the first part is defective, the probability the second part is also defective is 39/999 = .039. So our probability changes from trial to trial, but not very much. The probability distribution in this case would be the hypergeometric distribution, but it's not taught in this course. Since the probabilities do not change very much from trial to trial here, the binomial distribution can provide a reasonable approximation. As a rough guideline, the binomial distribution provides a reasonable approximation if we're not sampling more than 5% of the entire population. So, using the binomial distribution as an approximation, what is the probability of getting no more than 2 defective parts in our sample of 25?