Suppose the returns of a particular group of mutual funds ar

Suppose the returns of a particular group of mutual funds are normally distributed with a mean of 10.9% and a standard deviation of 4.6%. If the manager of a particular fund wants his fund to be in the top 10% of funds with the highest return, what return must his fund have?

Solution

mu =10.9%

sigma = 4.6%

For top 10% of the funds

z value is such that

P(Z<z) = 0.90

z = 1.28

X value = mu+1.28 (sigma)

= 16.788%

Hence his firm should have more than 16.788%