Distribution of a sample random variable

• I

Summary:

what distribution follows
$X_1, X_2, ..., X_{15}$ are independently to each other and follow $N (7, 3^2)$

what distribution the following statistics follow

$T = \frac{(\bar{X}− 7)}{\sqrt{s^2/15}}$

i know this follow t distribution $t_(n-1) =t_{14}$

but how do i find what distribution $T^2$ follows, can i just multiply it?

$T = (\frac{(\bar{X}− 7)}{\sqrt{s^2/15}})^2=\frac{Z^2*(n-1)}{\chi_{(n-1)}}$

Read your post before posting: use double $for ##\LaTeX## displayed math, not single$