Suppose a certain mutual fund has an annual rate of return t

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

Solution

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.