In the last quarter of 2007, a group of 64 mutual funds had a mean return of 1.6

Question

In the last quarter of 2007, a group of 64 mutual funds had a mean return of 1.61.6% with a standard deviation of 5.15.1%. Consider the Normal model N(0.0160.016,0.0510.051) 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.)

Explanation / Answer

mean return of 1.6% and tandard deviation of 5.1%.

mean = 0.016

Standard deviation = 0.051

a) What value represents the 40th percentile of these returns?

40th percentile =0.40

using Z table we calculate Z value = -0.25

So X= mean + Z* standard deviation

= 0.016 + (-0.25) *0.051

= 0.016 - 0.01275

=0.00325

is the 40th percentile value .

b) What value represents the 99th percentile?

40th percentile =0.99

using Z table we calculate Z value = 2.33

So X= mean + Z* standard deviation

= 0.016 + (2.33) *0.051

= 0.016 +0.11883

=0.13483

is the 99th percentile value

.

c) What's the IQR, or interquartile range, of the quarterly returns for this group of funds?

IQR = Q3 - Q1

For Q3=0.75

using Z table we calculate Z value = 0.67

So X= mean + Z* standard deviation

= 0.016 + (0.67) *0.051

= 0.016 +0.03417

=0.05017

is the 75th percentile value

For Q1=0.25

using Z table we calculate Z value =- 0.67

So X= mean + Z* standard deviation

= 0.016 + (-0.67) *0.051

= 0.016 -0.03417

= -0.01817

IQR =0.05017+0.01817

=0.06834

Is the IQR

a) The value that represents the 40th percentile is nothing%

40th percentile value is 0.00325

So 0.00325 *100 = 0.325

40th percentile is 0.32%

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