1. The World Health Organization reports that individuals, on average, eat approximately 267 insects a year. This population distribution takes only integer values (it can only take on whole numbers), so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 100 insects. Suppose that the standard deviation in the number of insects consumed is ?? = 490 and you take a random sample of 180 adults to gauge their self-reported insect consumption.

a) Without using numbers or formulas, first describe briefly what is the distribution of the population and what is the distribution of the sample average (i.e., sampling distribution). Do they look the same in the case of this problem?

b) What are the mean and the standard deviation of the population in the case of this problem?

c) What are the mean and standard deviation of the sampling distribution?

d) Use the central limit theorem (assume that n is sufficiently large so that the sampling distribution is approximately Normal) to find the probability that the average number of insects consumed for 180 randomly selected adults is greater than 300.

e) What are the mean and the standard deviation of the total number of insects consumed in your sample? In other words, calculate the mean and standard deviation of ?? = ??1 + ? + ??180, where Y is the total number of insects consumed in your sample and ??1 to ??180 are the random variables associated with each individual in your sample.