Answer
Confidence interval: $32.78\lt x ̅\lt37.42$
Work Step by Step
$n=40$, so:
$d.f.=n-1=39$
$level~of~confidence=(1-α).100$%
$90$% $=(1-α).100$%
$0.9=1-α$
$α=0.1$
$t_{\frac{α}{2}}=t_{0.05}=1.685$
(According to Table VI, for d.f. = 39 and area in right tail = 0.05)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=35.1-1.685\times\frac{8.7}{\sqrt {40}}=32.78$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=35.1+1.685\times\frac{8.7}{\sqrt {40}}=37.42$
