According to Investment Digest ("Diversification and the Risk/Reward Relationship", Spring 2011, 1-3), the mean of the annual return for common stocks from 1936 to 2011 was 15.4%, and the standard deviation of the annual return was 30.5%. During the same 74-year time span, the mean of the annual return for long-term government bonds was 5.2%, and the standard deviation was 6.0%. 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 12%.
b. Find the probability that the return for common stocks will be greater than 25%.