Question Help Consider a population of 1024 mutual funds that primarly invest in

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Question Help Consider a population of 1024 mutual funds that primarly invest in large companies, 6.50 and that o, the standard deviation, is 0.75. Complete (a) through (c) have determined that , te mean one year total percentage return achieved by all the funds, is a. According to the empirical rule, what percentage of these funds is expected to be within 12 standard deviations of the mean? b. [B(Round to two decimal places as needed.) c. According tothe Chebyshow rule, at least 88 89% of these funds are expected to have one-year total returns between what two amounts? Betweenand (Round to two decimal places as needed.) Enter your answer in each of the answer boxes. BOOKS STUDY TUTORS TEST PREP INTERNSHIPSSCHOLARSHIPS An institu. a

Explanation / Answer

In practical usage, in contrast to the 68–95–99.7 rule, which applies to normal distributions, Chebyshev'sinequality is weaker, stating that a minimum of just 75% of values must lie within two standard deviations of the mean and 89% within three standard deviations.

For the normal distribution, the values within onestandard deviation of the mean account for 68.27% of the set; while within two standard deviations account for 95.45%; and within three standard deviations account for 99.73%.

a) 95%

b) In probability theory, Chebyshev's inequality (also spelled as Tchebysheff's inequality, Russian: , also called Bienaymé-Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution's values can be more than k standard deviationsaway from the mean (or equivalently, at least 11/k2 of the distribution's values are within k standard deviations of the mean)

So, (1 -1/49) * 100 = 97.96%

c) 6.5 - 3 * 0.75 = 4.25

6.5 + 3 * 0.75 = 8.75

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