\(\displaystyle{x}^{{{2}}}_{\left\lbrace{1}-{0.025}\right\rbrace}={x}^{{{2}}}_{\left\lbrace{0.975}\right\rbrace}={16.047}\)

The boundaries of the confidence interval for the standart deviation are then:

\(\displaystyle\sqrt{{{\frac{{{n}-{1}}}{{{x}^{{{2}}}_{\left\lbrace{\frac{{\alpha}}{{{2}}}}\right\rbrace}}}}}}\dot{{\lbrace}}{s}=\sqrt{{{\frac{{{30}-{1}}}{{{45.722}}}}}}\dot{{\lbrace}}\sqrt{{{11.56}}}\approx{2.708}\)

\(\displaystyle\sqrt{{{\frac{{{n}-{1}}}{{{x}^{{{2}}}_{1}-{\left\lbrace{\frac{{\alpha}}{{{2}}}}\right\rbrace}}}}}}\dot{{\lbrace}}{s}=\sqrt{{{\frac{{{30}-{1}}}{{{16.047}}}}}}\dot{{\lbrace}}\sqrt{{{11.56}}}\approx{4.571}\)

2. The boundaries of the confidence interval for the variance is then the square of the boundaries of the confidence intervals for the standard deviation:

\(\displaystyle{\left({2.708}^{{{2}}},{4.571}^{{{2}}}\right)}={\left({7333},{50.894}\right)}\)