Question: Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent. Consider drawing a random sample of n=5 stocks from the population of all stocks and calculating the mean return, \(\bar{X}\), of the sampled stocks. Find the mean and the standard deviation of the sampling distribution of \(\bar{X}\), and find an interval containing 95.44 percent of all possible sample mean returns.