Answer
σ is between 2.133 and 3.093.
Work Step by Step
$\alpha=1-0.9=0.1.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=40-1=39$.
$X_{L}^2= X_{0.975}^2=26.509$
$ X_{R}^2= X_{0.025}^2=55.758$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(39)\cdot 2.55^2}{55.758}}=2.133$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(39)\cdot 2.55^2}{26.509}}=3.093.$
