For a given year, the rate of return on all stocks was normally distributed, with a mean of 15% and a standard deviation of 8%.
(a) An investor randomly chose one stock at the beginning of the year to hold for the course of the year. What is the probability that the rate of return on this stock was at least 5%?
(b) Another investor randomly chose 20 stocks at the beginning of the year to hold for the course of the year. What is the probability that the average rate of return on these stocks was at least 5%?