Chapter 8.1, Problem 4E

Consider a population consisting of the following five values, which represent the number of DVD rentals during the academic year for each of five housemates:

1. a. Compute the mean of this population.
2. b. Select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. Compute the mean for your sample.
3. c. Repeatedly select random samples of size 2, and compute the x value for each sample until you have the x values for 25 samples.
4. d. Construct a density histogram using the 25 $\bar{x}$ values. Are most of the 5c values near the population mean? Do the $\bar{x}$ values differ a lot from sample to sample, or do they tend to be similar? (Hint: See Example 8.1.)