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