Chapter 3, Problem 40PS

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.

a. According to the empirical rule what percentage of these funds is expected to be within $\pm 1$ standard deviation of the mean?

b. According to the empirical rule. what percentage of these funds is expected to be within $\pm 2$ standard deviations of the mean?

c. According to Chebyshev’s theorem. what percentage of these funds is expected to be within $\pm 1,\pm 2\text{ or }\pm 3$ standard deviations of the mean?

d. According to Chebyshev’s theorem, at least $93.75\%$ of these funds are expected to have one-year total returns between what two amounts?