Question

Consider a population of 10241024 mutual funds that primarily invest in large companies. You have determined that muμ​, the mean​ one-year total percentage return achieved by all the​ funds, is 7.407.40 and that sigmaσ​, the standard​ deviation, is 1.501.50. According to the Chebyshev​ rule, what percentage of these funds are expected to be within ​±3 standard deviations of the​ mean?

Answer 1

Answer to the question)

As per chebyshev's rule we get:

.

Where k denotes number of standard deviation

we need to find the percentage of mutual funds expected to be within 3 standard deviations of the mean as per this rule

then the percent is as follows

Percent = (1 - (1/k^2) ) *100
percent = (1 - (1/3^2) )* 100

Percent = (1 - 1/9)*100

Percent = (8/9)*100

Percent = 88.89%

[the value of mu and sigma is not used in this calculation as we directly make use of the Chebyshev rule which is based on only the number of standard deviations]