Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents.

a. How many different samples of two test grades are possible?

b. List all possible samples of size 2 and compute the mean of each.

c. Compute the mean of the sample means and compare it to the population mean.

d. If you were a student, would you like this arrangement? Would the result be different from dropping the lowest score? Write a brief report.