Distribution of a studentised single observation

Let $X_1,X_2,…,X_{100}$ be a random sample from a $N(2,4)$ population. Let $\overline X=\frac1{99}\sum_{i=1}^{99}X_i$, $S=\sqrt{\frac1{98}\sum_{i=1}^{99}(X_i-\overline X)^2}$ and $W=\dfrac{X_{100}-2}S$. Then the distribution of $W$ is