Consider a population of 1,024 mutual funds that primarily invest in large compa

Question

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

Explanation / Answer

a)According to the empirical rule 68% of these funds are expected to be within -/+1 standard deviation of the mean

b) According to the empirical rule, 95% of these funds are expected to be within -/+2 standard deviations of the mean

c)  According to the Chebyshev rule 0%  percentage of these funds are expected to be within -/+1 standard deviations

According to the Chebyshev rule 75%  percentage of these funds are expected to be within -/+2 standard deviations

According to the Chebyshev rule 88.89%  percentage of these funds are expected to be within -/+3 standard deviations

d)

for 93.75% are with in 4 std deviation away; hence values are (8.2-4*2.75 ; 8.2+4*2.75) =(-2.8 ; 19.2)

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