Question

According to Investment Digest (“Diversification and the Risk/Reward Relationship”, Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 16.5%, and the starndard deviation of annual return was 19%.

In later parts of the question we will ask:

a. What is the probability that the stock returns are greater than 0%?

b. What is the probability that the stock returns are less than 18%?

For this part, answer the following question:

Which table will we use to fine the area under the normal curve?

Answer 1

(a)

= 16.5

= 19

To find P(X:> 0):
Z = (0 - 16.5)/19

= - 0.8684

Since Z is negative, it lies on LHS of mid value.

Table of Area Under Standard Normal Curve gives area = 0.3078

So,

P(X > 0) = 0.5 + 0.3078 = 0.8078

So,

Answer is:

0.8078

(b)

To find P(X<18):

Z = (18 - 16.5)/19

= 0.0789

Since Z is positive it lies on RHS of mid value.

Table of Area Under Standard Normal Curve gives area = 0.0319

So,

P(X<18) = 0.5 + 0.0319 = 0.5319

So,

Answer is:

0.5319

(c)

To find the area under the normal curve, we will use, "TABLE: Area under the Normal curve from 0 to z", which is generally given at the end of Statistics books.