Consider a population of 1024 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 5.00 and that sigma, the standard deviation, is 3.00. Complete (a) through (c). a. According to the empirical rule, what percentage of these funds is expected to be within ±2 standard deviations of the mean? 95% b. According to the Chebyshev rule, what percentage of these funds are expected to be within ±2 standard deviations of the mean? nothing%

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joaobezerra joaobezerra · Answer 1 · 2020-05-14T04:33:15+02:00

Answer:

a) 95%

b) At least 75%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is at least [tex]100(1 - \frac{1}{k^{2}})[/tex].

a. According to the empirical rule, what percentage of these funds is expected to be within ±2 standard deviations of the mean?

95%

b. According to the Chebyshev rule, what percentage of these funds are expected to be within ±2 standard deviations of the mean?

At least 75%