Question

n the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 2.5​% with a standard deviation of 4.6​%. Consider the Normal model ​N(0.025​,0.046​) 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? (Please show work)

Answer 1

Given

Mean = 2.5% = 0.025

Standard deviation = 4.6% = 0.046

a)

The 40th percentile of these returns.

40 % means 0.40

From the standard normal distribution table we can get the Z-value

Z = -0.25

= 0.0135

b)

99th percentile means 0.99

From standard normal table

Z = 2.33

= 0.1322

c)

The​ IQR, or interquartile​ range, of the quarterly returns for this group of​ funds

IQR = Q₃ - Q₁

Q₃ means 75% = 0.75

Q₁ means 25% = 0.25

Again from standard normal table

Z value at 0.75 = 0.67

Z value at 0.25 = -0.67

At 75 % or Q3

0.67 = ( - 0.025) / 0.046

= 0.0558

At 25% or Q1

= -0.0058

IQR = Q3 - Q1

= 0.0558 - (-0.0058)

= 0.0616