In the last quarter of 2007, a group of 64 mutual funds had a mean return of 1.8% with a standard deviation of 4.5%. Consider the Normal model N(0.018,0.045) 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?
X : return of mutual funds.
X ~ N(0.018,0.045)
a).let x be the value that represents the 40th percentile of thesereturns.
according the the problem,
[ in any blank cell of excel type =NORMSINV(0.40)press enter]
the 40 th percentile = 0.66 % or 0.0066
b).let x be the value that represents the 99 th percentile of thesereturns.
according the the problem,
[ in any blank cell of excel type =NORMSINV(0.99)press enter]
the 99 th percentile = 12.27 % or 0.1227
c).for getting IQR, we have to calculate 25 th percentile and 75 the percentile.
let x be the value that represents the 25 th percentile of thesereturns.
according the the problem,
[ in any blank cell of excel type =NORMSINV(0.25)press enter]
the 25 th percentile = -0.012352
let y be the value that represents the 75 th percentile of thesereturns.
according the the problem,
[ in any blank cell of excel type =NORMSINV(0.75)press enter]
the 75 th percentile = 0.048352
The IQR be:-
or 6.07 %
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