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

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.

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