Question

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 1.9​% with a standard deviation of 6.3​%. Consider the Normal model ​N(0.019​,0.063​) for the returns of these mutual funds. ​
a) What value represents the 40th percentile of these​ returns? ​
b) What value represents the 99th​ percentile?
​c) What's the​ IQR, or interquartile​ range, of the quarterly returns for this group of​ funds?

Answer 1

Here

X ~ Normal(0.019, 0.063²)

a) To find 40th percentile of X i.e. x₁ such that

b) To find 99th percentile of X i.e. x₂ such that

c) To find 25th percentile of X i.e. x₃ such that

and

To find 75th percentile of X i.e. x₄ such that

So, Interquartile range =