A batch of 50 car batteries is scheduled to be shipped. However, the batch will only be shipped if a randomly selected sample of 5 batteries, sampled without replacement from the batch in such a way that every sample of size 5 has the same probability of being selected, has one or fewer defective batteries.
It is known that there are 6 defective batteries in the batch.
a) What are the possible values of the number of defective betteries in the sample?
b) What is the pribability the batch will be shipped?
c) What is the expected number of defective batteries in the sample?
d) What is the standard deviation of the number of defective batteries in the sample?