Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 8.5%, and the standard deviation of the annual return was 25.2%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 1.6%, and the standard deviation was 7.0%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario. 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 2%.
b. Find the probability that the return for common stocks will be greater than 11%.