How close is the confidence interval based on the normal approximation constructed in Exercise 20 to the

Question:

How close is the confidence interval based on the normal approximation constructed in Exercise 20 to the exact confidence interval constructed in Exercise 19?

The chi-square distribution is skewed, but as the number of degrees of freedom becomes large, the skewness diminishes. If the number of degrees of freedom, k, is large enough, the chi-square distribution is reasonably well approximated by a normal distribution with mean k and variance 2k.

Exercise 19

A sample of size 101 from a normal population has sample standard deviation s = 40.

Use Table A.4 to find the exact critical values X2 0.025 and X2 0.975 for a 95% confidence interval, and construct a 95% confidence interval for σ.
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