Answer
$74.6\lt\mu\lt86.8$
Work Step by Step
Based on the given data set, we can find $\bar X=80.7, s=11.74, n=12$
At the 90% confidence and $df=11$, the critical t-value is $t_{\alpha/2}=1.8$ (use table F)
the margin of error can be found as $E=1.8\times\frac{11.74}{\sqrt {12}}=6.1$
Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $74.6\lt\mu\lt86.8$
