Answer
$9.7\lt\mu\lt16.5$
Work Step by Step
Given $n=8, \bar X=13.1, s=4.1$, at a 95% confidence and $df=7$,
the critical t-value is $t_{\alpha/2}=2.37 $ (use table F)
The margin of error can be found as $E=2.37\times\frac{4.1}{\sqrt {8}}=3.4$
Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $9.7\lt\mu\lt16.5$