Answer
The results given by Fisher’s approximation are very close to those found in Table VII.
Work Step by Step
$z_{0.975}=-1.96$ and $z_{0.025}=1.96$
$v=100$
$X_{0.975}^2=\frac{(z_{0.975}+\sqrt {2\times100-1})^2}{2}=\frac{(-1.96+\sqrt {199})^2}{2}=73.772$
According to table VII: $X_{0.975}^2=74.222$ (d.f. = 100)
$X_{0.025}^2=\frac{(z_{0.025}+\sqrt {2\times100-1})^2}{2}=\frac{(1.96+\sqrt {199})^2}{2}=129.070$
According to table VII: $X_{0.025}^2=129.561$ (d.f. = 100)
