Suppose a certain mutual fund has an annual rate of return that is approximately
ID: 1256146 • Letter: S
Question
Suppose a certain mutual fund has an annual rate of return that is approximately normally distributed with mean 10 percent and standard deviation 4 percent.
The probability that the 1-year return will be negative is ______.
0.0170
0.0116
0.0062
0.0044
The probability that the 1-year return will exceed 15 percent is______.
0.1056
0.1357
0.8643
0.8944
The probability that the 1-year return will be negative is ______.
0.0170
0.0116
0.0062
0.0044
The probability that the 1-year return will exceed 15 percent is______.
0.1056
0.1357
0.8643
0.8944
Explanation / Answer
Let the mutual fund be X. The Mean is 10% and Standard Deviation is 4%.
X ~ N ( 0.10, 0.042)
Z = X - Mean / Standard Deviation
a ) The probability that the 1-year return will be negative is
P (X<0) = P (Z < 0 - 0.10 / 0.04)
= P (Z < -2.5)
Using value of Z=-2.5
P (X<-2.5) = 1 - 0.9938
= 0.0062
The probability that the 1-year return will be negative is 0.0062.
b ) The probability that the 1-year return will exceed 15 percent is
P (X>0.15) = P (Z > 0.15 - 0.10 / 0.04)
= P (Z > 1.25)
Using value of Z = 1.25
P (Z>1.25) = 1 - 0.8944
= 0.1056
The probability that the 1-year return will exceed 15 percent is 0.1056.
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