Question

For the second quarter (Q2) of 2014, a group of 127 mutual funds had a mean return of 3.1% with a standard deviation of 5%. A histogram shows the returns are unimodal and symmetric. Use the Empirical Rule (NOT the Normal calculator) to answer the following questions. (In other words, enter approximate answers to these questions based on the Empirical Rule instead of exact answers from the Normal calculator.) (Enter all your numeric answers to two decimal places.)

(a) What percent of mutual funds have a return greater than 3.1%?

%

(b) What percent of mutual funds have a return between -11.9% and 18.1%?

%

(c) What percent of mutual funds have a return greater than 8.1%?

%

(d) What percent of mutual funds have a return less than -6.9%?

%

Answer 1

1) Since histogram shows the returns are unimodal and symmetric and mean return is 3.1%

So   mutual funds have a return greater than 3.1%

2) We know by Empirical Rule  68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

Also,

So mutual funds have a return between -11.9% and 18.1%

3) Since , and 68.27% of the values lie within one standard deviation of the mean.

Now,  

Hence   of mutual funds have a return greater than 8.1%

4) As and 95.45% of the values lie within two standard deviation of the mean.

As,

Hence   of mutual funds have a return less than -6.9%