A researcher developed a regression model to predict the final exam score $\left(y\right)$ based on the number of hours studied $\left(x\right)$. The regression equation is $\hat{y}=50+2x$. The sample size is $n=16$, the mean number of hours studied is $\bar{x}=10$, $S_{xx}=240$, and the standard error of estimate is $s_y=5$. Construct a $90\%$ prediction interval for the final exam score when a student studies for $14$ hours.