Refer to Exercise 10. Use the normal approximation to estimate the critical values 2 100, 0.025

Refer to Exercise 10. Use the 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.

A more accurate normal approximation to χ²_k,α is given by χ²_k,α ≈ 0.5(z_α +√2k − 1)², where z_α is the z-score that has area α to its right.

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.