The procedure is vague as to whether the sampling is done with replacement or without replacement. If the sampling is done with replacement, then the number X of individuals who answer "yes" is a binomial random variable. On the other hand, because here the population has finite size, if the sampling is done without replacement, then X is a hypergeometric random variable. When the sample size is small relative to the population size, the difference between the hypergeometric and binomial distributions is negligible. A common rule is that the sample size should be no more than 5% the population size. However, in this particular question, the sample is size 400, which exceeds 5% of the population size (7500). So the hypergeometric should be kept when the sampling is without replacement.

In short, the answer here depends on whether the sampling is with or without replacement.

Marc N.

09/26/19