Question

The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.1%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. Use Table 1 in Appendix B.

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)?

Answer 1

Ans:

mean=14.1

standard deviation=4.4

a)

z=(20-14.1)/4.4

z=1.34

P(z>=1.34)=0.0901

b)

z=(10-14.1)/4.4

z=-0.932

P(z<-0.932)=0.1757

c)

P(Z>z)=0.1

P(Z<=z)=1-0.1=0.9

z=1.282

x=14.1+1.282*4.4=19.74