Answer
σ is between 2.9 and 6.9.
Work Step by Step
The mean can be counted by summing all the data and dividing it by the number of data: $\frac{62+61+...+67}{12}=60.67.$
Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(62-60.67)^2+...+(67-60.67)^2}{11}}=4.075.$
$\alpha=1-0.95=0.05.$ By using the table we can find the critical chi-square values with with $df=sample \ size-1=12-1=11$.
$X_{L}^2= X_{0.975}^2=3.816$
$ X_{R}^2= X_{0.025}^2=21.92$
Hence the confidence interval:$\sigma$ is between $\sqrt{\frac{(n-1)\cdot s^2}{ X_{R}^2}}=\sqrt{\frac{(11)\cdot 4.075^2}{21.9}}=2.9$ and $\sqrt{\frac{(n-1)\cdot s^2}{ X_{L}^2}}=\sqrt{\frac{(11)\cdot 4.075^2}{3.816}}=6.9.$
