Consider a population of 1,024 mutual funds that primarily invest in large companies. You have determined that µ, the mean one-year total percentage return achieved by all the funds, is 8.20 and that µ, the standard deviation, is 2.75.
a. According to the empirical rule, what percentage of these funds is expected to be within ± 1 standard deviation of the mean?
b. According to the empirical rule, what percentage of these funds is expected to be within ±2 standard deviations of the mean?
c. According to the Chebyshev's rule, what percentage of these funds is expected to be within ±1, +2, or ±3 standard deviations of the mean?
d. According to the Chebyshev's rule, at least 93.75% of these funds are expected to have one-year total returns between what two amounts?