For the chi-squared distribution, the mean equals df and the standard deviation equals √22(df).
a. Explain why, as a rough approximation, for a large df value, 95% of the chi-squared distribution falls within df ± 2 √2(df).
b. With df = 8, show that df ± 2 √2(df) gives the interval (0, 16) for approximately containing 95% of the distribution. Using the chi-squared table, show that exactly 95% of the distribution actually falls between 0 and 15.5.