11.86 Variability of chi-squared For the chi-squared distribution, the mean equals df and the standard deviation equals 221df2.

a. Explain why, as a rough approximation, for a large df value, 95% of the chi-squared distribution falls within df { 2221df2.

b. With df = 8, show that df { 2221df2 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.