Answer
$13.5\lt\mu\lt16.5$
$16.5$ miles per hour.
Work Step by Step
Given $n=13, \bar X=15.0, s=1.7$, at the 99% confidence and $df=12$,
the critical t-value is $t_{\alpha/2}=3.1 $ (use table F)
The margin of error can be found as $E=3.1\times\frac{1.7}{\sqrt {13}}=1.5$
Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $13.5\lt\mu\lt16.5$
The highest speed the meteorologist likely to use is $16.5$ miles per hour.
