Assume that the birthweights of babies born into low socioeconomic status are normally distributed with a mean of 116 oz and a standard deviation of 18 oz. We generate 100 random samples, each consisting of 100 birthweights from this distribution. For each sample, the null and alternative hypotheses on mean birthweight mu (H0: mu = 120; H1: mu < 120) are posed for the appropriate one-tailed t-test at a 5% level of significance. Consider the number of samples k where H0 is accepted.

a) What probability distribution does k follow?

b) Calculate the population mean and variance for k.

c) What is the probability of obtaining a value of k that is 20 or less?