Chapter 5.6, Problem 5E

Let $X_1,X_2,\mathrm{...},X_{18}$ be a random sample of size 18 from a chi-square distribution with $r=1$.

Recall that $\mu =1$ and ${\sigma }^2=2$.

(a) How is $Y={\displaystyle {\sum }_{i=1}^{18}{X}_i}$ distributed?

(b) Using the result of part (a), we see from Table IV in Appendix B that

$P\left(V\le 9.390\right)=0.05$ and $P\left(V\le 34.80\right)=0.99$.

Compare these two probabilities with the approximations found with the use of the central limit theorem.