Question

Assume that annual returns on large-company stocks are normally distributed with an average historical return of 12.3% and a standard deviation of 20.0%. What is the probability that annual return on large-company stocks is greater than 5% and Less than 30%?

Answer 1

Solution:

Given: Annual returns on large-company stocks are normally distributed with an average historical return of 12.3% and a standard deviation of 20.0%.

Thus Mean = and standard deviation =

We have to find the probability that annual return on large-company stocks is greater than 5% and Less than 30% .

That is:

P( 5 < X < 30 ) = ..........?

Find z scores for x = 5 and for x= 30

and

Thus we get:

P( 5 < X < 30 ) = P( -0.37 < Z < 0.89)

P( 5 < X < 30 ) = P( Z < 0.89) - P(Z < -0.37)

To find P( Z < 0.89) and P(Z < -0.37) , look in z table for z = 0.8 and 0.09 as well as for z = -0.3 and 0.07 and find corresponding area.

P( Z < 0.89) = 0.8133

P( Z < -0.37 ) =0.3557

Thus

P( 5 < X < 30 ) = P( Z < 0.89) - P(Z < -0.37)

P( 5 < X < 30 ) = 0.8133 - 0.3557

P( 5 < X < 30 ) = 0.4576

Thus the probability that annual return on large-company stocks is greater than 5% and Less than 30% is 0.4576