Question

Suppose that returns for Firm X are normally distributed with a mean of 12% and a standard deviation of 10%. Assuming that this distribution is maintained into the future, respond to the following questions. A. What is the probability of occurrence of a return less than 2 %? Make a sketch showing your answer as an area under the normal curve. B. What is the probability of occurrence of a return greater than 32%? Make a sketch showing your answer as an area under the normal curve.

Answer 1

A.

Mean=12 percent

Standard Deviation=10 percent

When return is=2 percent

D=(2-12)/10=-1

Referring to Cumulative area under the Standard Normal Distribution Table:

For D=-1.00 N(d) =Area under Standard Normal Distribution Table =0.1587

Probability of occurrence of a return less than 2%=0.1587=15.87%

B.

Mean=12 percent

Standard Deviation=10 percent

When return is =32 percent

D=(32-12)/10=2

Referring to Cumulative area under the Standard Normal Distribution Table:

For D=-2.00 N(d) =Area under Standard Normal Distribution Table =0.9772

Probability of occurrence of a return less than 32%=0.9772=97.72%