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 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.9%. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)? What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less (to 4 decimals)? 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

Given, mean =14.4% and std deviation = 4.9%

a. P(X>=20%)                          Z=(X-14.4)/4.9 Z follows standard normal

= 1- P(X<20)

= 1- P(Z<(20-14.4)/4.9)

=1- P(Z<1.143)

=1-0.8729

=0.1271

reqd probability = 0.1271

b. P(X<=10)

= P(Z<= 10-14.4/4.9)

=P(Z<= -.898)

=0.1841

c.

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