Distribution of a sample random variable

[fiksx]

TL;DR

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

 

[BvU]

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