In the last quarter of 2007, a group of 64 mutual funds had a mean return of 2.2 2.2% with a standard deviation of 6.3 6.3%. Consider the Normal model N( 0.022 0.022, 0.063 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? a) The value that represents the 40th percentile is nothing %. (Round to two decimal places as needed.)

For the 40th percentile, we look in a z chart. We want to find the value as close to 0.40 as we can get; this is 0.4013, and it corresponds to a z score of z = -0.25.

Our formula for a z score is [tex]z=\frac{X-\mu}{\sigma}[/tex]. Using our values, we have

-0.25 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(-0.25) = X-2.2

-1.575 = X-2.2

Add 2.2 to each side:

-1.575+2.2 = X-2.2+2.2

0.625 = X

For the 99th percentile, the value in the z chart closest to 0.99 is 0.9901, which corresponds to a z score of z = 2.33:

2.33 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(2.33) = X-2.2

14.679 = X-2.2

Add 2.2 to each side:

14.679+2.2 = X-2.2+2.2

16.879 = X

For the IQR, we find the values for the 75th percentile (Q3) and the 25th percentile (Q1). The value in a z chart closest to 0.75 is 0.7486, which corresponds to a z score of z = 0.67:

0.67 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(0.67) = X-2.2

4.221 = X-2.2

Add 2.2 to each side:

4.221+2.2 = X-2.2+2.2

6.421 = X

The value in a z chart closest to 0.25 is 0.2514, which corresponds to a z score of z = -0.67:

-0.67 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(-0.67) = X-2.2

-4.221 = X-2.2

Add 2.2 to each side:

-4.221+2.2 = X-2.2+2.2

-2.021 = X

This makes the interquartile range

6.421--2.021 = 8.442

AFOKE88 AFOKE88 · Answer 2 · 2022-04-07T12:08:44+02:00

The 40th percentile, the 99th percentile and the Interquartile range are; a) 0.625 b) 16.879 c) 8.442

What is the interquartile range?

We are given;

Mean; μ = 2.2

Standard deviation; σ = 6.3

A) The z-score from online tables for a 40th percentile is;

z = -0.25

From formula of z-score, we have;

-0.25 = (x' - 2.2)/6.3

6.3(-0.25) = x' - 2.2

-1.575 = x' - 2.2

x' = 0.625

B) The z score of 99th percentile is; z = 2.33.

Thus;

2.33 = (x' - 2.2)/6.3

6.3(2.33) = x' - 2.2

14.679 = x' - 2.2

x' = 16.879

C) The z-score for the 75th percentile is approximately; z = 0.67:

Thus;

0.67 = (x' - 2.2)/6.3

6.3(0.67) = x' - 2.2

4.221 = x' - 2.2

x' = 6.421

The z-score for the 25th percentile is z = -0.67:

Thus;

-0.67 = (x' - 2.2)/6.3

6.3(-0.67) = x' - 2.2

-4.221 = x' - 2.2

-2.021 = x'

Thus, interquartile range is;

IQR = 6.421- (-2.021)

IQR = 8.442

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