Answer
df=49, $X_{L}^2=32.357$, $ X_{R}^2=71.42$, $\sigma$ is between 0.4862 and 0.7224.
Work Step by Step
$\alpha=1-0.95=0.05.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=50-1=49$.
$X_{L}^2= X_{0.975}^2=32.357$
$ X_{R}^2= X_{0.025}^2=71.42$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(49)\cdot 0.587^2}{71.42}}=0.4862$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(49)\cdot 0.587^2}{32.357}}=0.7224.$
