Researchers analyzed the relationship between the average price of a used car (in units of thousands of dollars) and the average price of a new car (in units of thousands of dollars) over $12$ years. The regression equation is $\hat{y}=5.2+0.6x$, with $\bar{x}=28$, $\bar{y}=21$, $\sum (x_i-\bar{x}{)}^2=144$, and $s_e=1.8$. Find the $95\%$ prediction interval for the average used car price when the new car price is $\$32,000$. (Use $t_{10,0.025}=2.228$).