Question

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 3.8​% with a standard deviation of 4.2​%. 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. Be sure to draw a picture first. ​

a) Returns of negative −4.6​% or less ​

b) Returns of 3.8​% or less ​

c) Returns between negative −0.4​% and 8.0​% ​

d) Returns of more than 16.4​%

Answer 1

Here we have

Following is the graph:

a)

Since according to the​ 68-95-99.7 rule 95% data values lies within 2 standard deviation of mean so area between -4.6 and 3.8% is

0.95 /2 = 0.475

That is area below -4.6% is 0.5 - 0.475 = 0.025. That is the probability of Returns of negative −4.6​% or less is 2.5%.

Answer: 0.025

b)

Since mean is 3.8% so the probability of Returns of 3.8% or less is 0.50.

Answer: 0.50

c)

The probability that return is between negative −0.4​% and 8.0​% is 0.68 or 68%.

d)

Area above 16.4% is (1-0.997) /2 = 0.0015

SO the required probability is 0.0015.