Suppose $X_1,...,X_5$ and $Y_1,...,Y_{10}$ are random samples from an independent $N(2,5)$ and $N(2,30)$, respectively. Let $\overline X$ and $\overline Y$ denote the samples means and $S^2$ denotes the sample variance.
The question is,
a) Find a constant $c$ such that $P(\frac{\overline X-2}{S}<c)=0.90$
b)Find a constant $d$ such that $P(S>d)=0.99$
Part (a) is okay for me (which is a T-distribution with degree of freedom $n-1=4$)
But Part(b) is quite confusing to me, is the $S$ (sample variance) refers to $\overline X$ or $\overline Y$? How should I start with this question?