In the last quarter of 2007, a group of 64 mutual funds had a mean return of 4 2

Question

In the last quarter of 2007, a group of 64 mutual funds had a mean return of 4 2% with a standard deviation of 5.2%. 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 usirg technology to find the values more precisely Be sure to draw a picture first a) Returns of - 1.0% or less b) Returns of 4 2% or more c) Returns between - 11.4% and 19.8% d) Returns of less than - 6 2% a) The expected percentage of returns that are - 1.0% or less is %.

Explanation / Answer

-1=4.2-5.2

Hence we need the probability of P(Z<-1)

We know that 68% of data lies between -1<Z<1

Hence P(Z<-1)+P(Z>1)=1-0.68=0.32

Hence P(Z<-1)=0.32/2=0.16=16%

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