Student t from an extra normal

Let $X_{1},X_{2},…,X_{9},Y$ be independent and identically distributed $N(\mu,\sigma^{2})$ random variables. Define $\bar{X}=\frac{1}{9}\sum_{i=1}^{9}X_{i}$, $S^{2}=\frac{1}{8}\sum_{i=1}^{9}(X_{i}-\bar{X})^{2}$. The distribution of $\dfrac{3}{\sqrt{10}}\left(\dfrac{\bar{X}-Y}{S}\right)$ is