Please explain how you compute these answers given for A,B,C. Objective:Apply th
ID: 2948217 • Letter: P
Question
Please explain how you compute these answers given for A,B,C. Objective:Apply the empirical rule and the Chebyshev rule. Consider a population of 1024 mutual funds that primarily invest in large companies You have determined that p, the mean one-year total percentage return achieved by all the funds, is 9.20 and that o, the standard deviation, is 1 25. 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? 99.7 % b. According to the Chebyshev rule, what percentage of these funds are expected to be within ±2 standard deviations of the mean? 75 % (Round to two decimal places as needed.) c. According to the Chebyshev rule, at least 88.89% of these funds are expected to have one-year total returns between what two amounts? Between 5.45 and 12.95 (Round to two decimal places as needed.)
Explanation / Answer
a) According to the empirical rule, 99.7 % of the observations lies within 3 standard deviations from the mean. Therefore 99.7% is correct here.
b) According to Chebyshev's inequality theorem, at least 1 - 1/k2 of the observations lies within k standard deviations from the mean. Therefore at least 1 - 1/22 = 75% of the observations lies within 2 standard deviations from the mean. Therefore 75% is correct here.
c) Now here we are given that at least 88.89% of the observations lies within what interval.
88.89% is 8/9
1 - 1/k2 = 8/9
1/k2 = 1 - 8/9
k = 3 here.
Therefore we just need to find the interval as:
Mean - 3*Std Dev and Mean + 3*Std Dev
9.2 - 3*1.25 = 5.45 and 9.2 + 3*1.25 = 12.95
Therefore they lie between 5.45 and 12.95