Consider a population of 1024 mutual funds that primarily invest in large compan

Question

Consider a population of 1024 mutual funds that primarily invest in large companies. You have determined that u, the mean one-year total percentage return achieved by all the funds, is 8.70 and that o, the standard deviation, is 125. Complete (a) through (c) a According to the empirical rule, what percentage of these funds is expected to be within :3 standard deviations of the mean? D- b. According to the Chebyshev rule, what percentage of these funds are expected to be within +2 standard deviations of the mean? D% (Round to two decimal places as needed ) c According to the Chebyshev rule, at least 93 75% of these funds are expected to have one-year total returns between at two amounts? Between and (Round to two decimal places as needed.)

Explanation / Answer

a) P(within +3 sd of the mean) = P(-3 < Z < 3) = 99.7%

b) P(within +2 sd of the mean) = 1 - 1/22 = 0.75 = 75%

c) P(within +k sd of the mean) = 1 - 1/k2

1 - 1/k2 = 0.9375

or, k = 4

Mean + 4 * sd = 8.7 + 4 * 1.25 = 3.7 , 13.7

Between 3.7 and 13.7

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