Use the Cash 5 dataset on the companion website for this exercise, with data from 1560 games of Pennsylvania's Cash 5 lottery game described in Section 9.10. The variables High and Low give the highest and lowest numbers picked in each game.
a. For each game, find R = High 2 Low, the range between the highest and lowest numbers. Draw a histogram of R, and describe the shape of this histogram.
b. Find the mean for each of the variables R, High and Low. Verify that the mean for R equals the difference between the means for High and Low.
c. What is the maximum possible value of the range R in the Cash 5 game? What values of High and Low would lead to this value?
d. Tally how often each value of R occurred in the 1560 games given in the dataset. How often did the maximum possible value of R occur?