In the last quarter of 2007, a group of 64 mutual funds had a mean return of 5.1

Question

In the last quarter of 2007, a group of 64 mutual funds had a mean return of 5.15.1% with a standard deviation of 5.35.3%. 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 21.021.0% or moremore b) Returns of 5.15.1% or lessless c) Returns between negative 0.20.2% and 10.410.4% d) Returns of moremore than 15.715.7%

Explanation / Answer

a) Returns of 21.0 % or more =P(X>21) =P(Z>(21-5.1)/5.3)=P(Z>3) from empirical rule:

P(Z>3) =(1-0.997)/2=0.0015 ~ 0.15%

b) Returns of 5.1 % or less =P(Z<(5.1-5.1)/5.3)=P(Z<0)=0.5

c) P(-0.2<X<10.4)=P((-0.2-5.1)/5.3<Z<(10.4-5.1)/5.1)= P(-1<Z<1) =0.68 ~ 68%

d)P(X>15.7)=P(Z>(15.7-5.1)/5.3)=P(Z>2) =(1-0.95)/2 =0.025 ~ 2.5%

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.