Question

In the last quarter of 2007, a group of 64 mutual funds had a mean return of 3.2% with a standard deviation of 4.6%. If a normal model can be used to model them, what percent of the funds would you expect to be in each region? Use the 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely.

Answer 1

Answer)

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

Given mean = 3.2

S.d = 4.6

So, 68% lies in between (3.2-4.6) and (3.2+4.6) or -1.4 and 7.8

95% lies in between 3.2-(4.6*2) and 3.2+(4.6*2) that is in between -6 and 12.4

99.7% lies in between 3.2-(4.6*3) and 3.2+(4.6*3) that is in between -10.6 and 17