Refer to Exercise 10. Use the more accurate normal approximation to estimate the critical values 2

Refer to Exercise 10. Use the more accurate normal approximation to estimate the critical values χ²_{100, 0.025} and χ²_{100, 0.975} for a 95% confidence interval, and construct a 95% confidence interval for σ.

Refer to Exercise 10.

A sample of size 101 from a normal population has sample standard deviation s = 40. The lower and upper 0.025 points of the χ²₁₀₀ distribution are χ²_{100, 0.975} = 74.222 and χ²_{100, 0.025} = 129.561. Use these values to construct a 95% confidence interval for σ.