Question

The average return for large-cap domestic stock funds over the three years 2009–2011 was 14.8%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.5%.

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

Solution:
Given in the question
Population proportion = 0.148
Standard deviation = 0.045

Solution(a)
P(Xbar>0.2)=1-P(Xbar<0.2)
Z = (0.2-0.148)/0.045 = 1.1555
so from the z table we found p-value
P(Xbar>0.2) = 1- 0.8770 = 0.123
So there is 12.3% probability of an individual cap domestic stock fund has a three year return of at 20%.

Solution(b)
P(Xbar<=0.1)=?
Z = (0.1-0.148)/0.045 = -1.066
So from Z table we found
P(Xbar<=0.1) = 0.1423
So there is 14.23% probability an individual large cap domestic stock fund had a three year return of 10% or less.
Solution(c)
if p= 0.9
So Z= 1.29
1.29 = (X-0.148)/0.045
0.05805 = X-0.148
X = 0.05805 +0.148 = 0.20605

SO there is 20.61% return have to be to put a domestic stock fund in the top 10% for the three year period.