In the last quarter of 2007, a group of 64 mutual funds had a mean return of 5.5% with a standard deviation of 7.4%. 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 1.9% or less b) Returns of 5.5% or more c) Returns between negative 9.3% and 20.3% d) Returns of more than 27.7% a) The expected percentage of returns that are negative 1.9% or less is nothing%. (Type an integer or a decimal.) b) The expected percentage of returns that are 5.5% or more is nothing%. (Type an integer or a decimal.) c) The expected percentage of returns that are between negative 9.3% and 20.3% is nothing%. (Type an integer or a decimal.)
a)
probability =P(X<-1.9)=(Z<(-1.9-5.5)/7.4)=P(Z<-1)=0.16 ~ 16% |
b)
probability =P(X>5.5)=P(Z>(5.5-5.5)/7.4)=P(Z>0)=1-P(Z<0)=1-0.5=0.5~ 50.0% |
c)
probability =P(-9.3<X<20.3)=P((-9.3-5.5)/7.4)<Z<(20.3-5.5)/7.4)=P(-2<Z<2)=0.95~ 95.0% |
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