Answer
$38.4\lt\mu\lt44.8$
Work Step by Step
Given $n=24, \bar X=41.6, s=7.5$, at a 95% confidence and $df=23$,
the critical t-value is $t_{\alpha/2}=2.07 $ (use table F)
The margin of error can be found as $E=2.07\times\frac{7.5}{\sqrt {24}}=3.2$
Thus, the interval of the true mean can be estimated as
$\bar X-E\lt\mu\lt\bar X+E$ which gives $38.4\lt\mu\lt44.8$
