The average return for large-cap domestic stock funds over the three years 2009–

Question

The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.2%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.9%.

20.48

a. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)?

b. What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less (to 4 decimals)?

c. How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period (to 2 decimals)?

Explanation / Answer

Let X is a Random Variable denoting 'three-year return of an individual large-cap domestic stock fund' . Then by question X is normally distributed with mean 14.2 and variance 4.9*4.9 = 24.01

X~N(14.2,24.01)

a) X>20 =
1-P(X<20)=1-0.8817=0.1183

b) X<10=0.1957
c)P(X>c) =0.1 , c=?
so , c= 7.920%

Normal random variable's probalities are calculated using biometrika table.

X~N(a,b2) ==> Z=(X-a)/b~N(0,1)
bIOMETRIKA TABLE FOR CALCULATING PROBAILITIES OF Z IS USED TO CALCULATE ANY NORMAL PROBAIBLITY.

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