Answer
σ is between 0.57 and 0.72.
Work Step by Step
$\alpha=1-0.9=0.1.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=106-1=105$.
$X_{L}^2= X_{0.975}^2=77.929$
$ X_{R}^2= X_{0.025}^2=124.342$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(105)\cdot 0.62^2}{124.342}}=0.57$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(105)\cdot 0.62^2}{77.929}}=0.72.$
