In the last quarter of? 2007, a group of 64 mutual funds had a mean return of 2.

Question

In the last quarter of? 2007, a group of 64 mutual funds had a mean return of 2.1?% with a standard deviation of

7.1?%. 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 9.2% or more

b) Returns of 2.1% or more

c) Returns between -19.2%and 23.4%

d) Returns of less than -12.1%

Explanation / Answer

Please see below the answers: -

a)

z=9.2-2.1/7.1

z=1

Looking at the z-table, we get the value as 0.84134. Hence, greater than that would be 1-0.84134=0.15866

b)

2.1 would be z=0. Hence, 50%.

c)

z=-19.2-2.1/7.1

z=-3

z=23.4-2.1/7.1

z=3

Looking at the z-table, we get the value as 0.00135 and 0.99865. Hence, the area in between would be 0.99865-0.00135=0.9973

d)

z=-12.1-2.1/7.1

z=-2

0.2275

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