Question

You may need to use the appropriate appendix table to answer this question. 

The average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. 

(a) What is the probability an individual large-cap domestic stock fund had a three-year return of at least 17%? 

(b) What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less?

(c) How big does the return have to be to put a domestic stock fund in the top 25% for the three-year period? 

Answer 1

a)
Here, μ = 14.4, σ = 4.4 and x = 17. We need to compute P(X >= 17). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (17 - 14.4)/4.4 = 0.59

Therefore,
P(X >= 17) = P(z <= (17 - 14.4)/4.4)
= P(z >= 0.59)
= 1 - 0.7224 = 0.2776

b)
P(X <= 10) = P(z <= (10 - 14.4)/4.4)
= P(z <= -1)
= 0.1587

c)
z-value = 0.67

x = 14.4 + 0.67*4.4
x = 17.348

Ans: 17.35 %