We assume the probability of being born in the winter (as opposed to spring, summer, or fall) is 0.25, and the random variable X counts the number of people born in the winter when we take a sample of a given size.
a. In which case is X approximately binomial: when we sample 5 from 10 people, when we sample 5 from 100 people, or both, or neither?
b. If we sample 100 people, on average how many do we expect to have been born in the winter?
c. For any sample size, on average what proportion of people do we expect to have been born in the winter?