(a) Take a random sample of 20 sizes of men from a binomial distribution (the size corresponds to the number of successes of n independent Bernoulli experiments with chance of success p) with parameters n = 142 and p = 0.5, and a distinct random sample of 20 women's heights from a binomial distribution with parameters n = 130 and p = 0.5. From these data, give an estimate of the average height of adults and calculate the margin of error on the estimate. (b) Take an SRS of 40 adult heights from a binomial distribution with parameters n = 135 and p = 0.5. From these data, give an estimate of the average height of all adults and give a margin of error on the estimate. (c) Compare the results of (a) and (b). Discuss cases where stratification appears to produce gains in precision of estimates.