Refer to the population of billionaires. Select 100 random samples of size n = 5 from this population [Excel instructions]. Use the last four digits of your SSN as the Random Seed when generating random numbers.

        1) Compute the mean and variance of each sample.
        2) Construct a histogram of the original population, and then of the 100 sample means. Write a short paragraph
        comparing and contrasting these distributions.
        3) Compute the mean of the population and the mean of the 100 sample means. Are the values similar? Should they be?
        4) Repeat parts 1-3 using 100 samples of size n = 30. How are the results different?
        5) Explain briefly what you would expect to happen to each characteristic of the sampling distribution of the sample mean
        if you took more samples (say 500, or 1000), with the size of each sample remaining fixed.
            a) the mean of the sampling distribution.
            b) the variance of the sampling distribution.
            c) the shape of the sampling distribution.