54. The American Association of Individual Investors publishes an annual guide to the top mutual funds (The Individual Investor’s Guide to the Top Mutual Funds, 22e, American Association of Individual Investors, 2003). Table 5.8 contains their ratings of the total risk for 29 categories of mutual funds.

a. Let x  1 for low risk up through x  5 for high risk, and develop a probability distribution for level of risk.

b. What are the expected value and variance for total risk?

c. It turns out that 11 of the fund categories were bond funds. For the bond funds, 7 categories were rated low and 4 were rated below average. Compare the total risk of the bond funds with the 18 categories of stock funds.