3.47 Are the data Normal? Returns on stocks. The return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. Exercise 1.32 provides a histogram of the distribution of the monthly returns for all stocks listed on U.S. markets from January 1985 to December 2015 (372 months). Excluding the three low outliers, the average return of the remaining 369 months is 0.840% with a standard deviation of 4.097%.13 STOCKS

(a) If the distribution of the 369 months (excluding the outliers) were exactly N(0.84, 4.097), what would be the proportion of months with returns greater than 0? Greater than 4%?

(b) What proportion of the actual returns are greater than 0? Greater than 4%? Do these results suggest that the N(0.84, 4.097) provides a good approximation to the distribution of returns over this period?