Chapter 3, Problem 3.34AC

Consider a population of 1,024 mutual funds that primarily invest in large companies. You have determined that $\mu$, the mean one-year total percentage return achieved by all the funds, is 8.20 and that $\sigma$, the standard deviation, is 2.75.

1. According to the empirical rule, what percentage of these funds is expected to be within $\pm 1$ standard deviation of the mean?
2. According to the empirical rule, what percentage of these funds is expected to be within $\pm 2$ standard deviations of the mean?
3. According to the Chebyshev rule, what percentage of these funds is expected to be within $\pm 1,\pm 2,\text{or}\pm 3$ standard deviations of the mean?
4. According to the Chebyshev rule, at least 93.75% of these funds are expected to have one-year total returns between what two amounts?