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 14.3% Assume the three-year returns were normally distributed across funds with a standard deviation of 4.7%

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

Ans:

Given that

mean=14.3

standard deviation=4.7

a)P(X>=20)

z=(20-14.3)/4.7=1.213

P(z>=1.213)=1-0.8874=0.1126

b)P(X<=10)

z=(10-14.3)/4.7=-0.915

P(z<=-0.915)=0.1801

c)P(Z>=z)=0.1

P(Z<=z)=0.9

z=1.282

x=14.3+1.282*4.7

x =14.3+6.025=20.325

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