Question

According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stock from 1926 to 1992 was 16.5%, and the standard deviation of the 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%?
What is the probability that the stock returns are less than 18%?

For this part, answer the following question:
What is the area between the mean and our actual score?

Answer 1

Population mean, µ = 16.5 %

Population standard deviation, σ = 19 %

Probability that the stock returns are greater than 0% =

= P( X > 0)

= P((X - µ)/σ > (0 - 16.5)/19)

= P(z > -0.87)

= 1- P( z < -0.87)

Using excel function:

= 1- NORM.S.DIST(-0.87, TRUE)

= 0.8074

The area between the mean and the actual score 0 = 0.8074 - 0.5000 = 0.3074

Probability that the stock returns are less than 18% =

= P( X < 18)

= P( (X - µ)/σ < (18 - 16.5) /19)

= P( z < 0.08)

Using excel function:

= NORM.S.DIST(0.08, TRUE)

= 0.5319

The area between the mean and the actual score 18 = 0.5319 - 0.5000 = 0.0319