# Probability: Normally Distributed Variables – #61

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 13.4%, and the standard deviation of the annual return was 20.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 7.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

a. Find the probability that the return for common stocks will be greater than 0%.

b. Find the probability that the return for common stocks will be less than 0%.

c. Find the probability that the return for common stocks will be less than 10%.

d. Find the probability that the return for common stocks will be greater than 20%.

e. Find the probability that the return for common stocks will be greater than 30%.

f. Find the probability that the return for common stocks will be less than -10%. 