Answer
Confidence interval: $97.07\lt x ̅\lt111.53$
Work Step by Step
$n=15$, so:
$d.f.=n-1=14$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.9=1-α$
$α=0.1$
$t_{\frac{α}{2}}=t_{0.05}=1.761$
(According to Table VI, for d.f. = 14 and area in right tail = 0.05)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=104.3-1.761\times\frac{15.9}{\sqrt {15}}=97.07$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=104.3+1.761\times\frac{15.9}{\sqrt {15}}=111.53$
