Answer
Confidence interval: $87.01\lt x ̅\lt99.85$
We are 99% confident that the mean amount of money spent per person at the park is between $\$87.01$ and $\$99.85$.
Work Step by Step
We want to estimate the mean using a sample whose size is greater than 30.
$n=40$, so:
$d.f.=n-1=39$
$level~of~confidence=(1-α).100$%
$99$% $=(1-α).100$%
$0.99=1-α$
$α=0.01$
$t_{\frac{α}{2}}=t_{0.005}=2.708$
(According to Table VI, for d.f. = 39 and area in right tail = 0.005)
$Lower~bound=x ̅-t_{\frac{α}{2}}.\frac{s}{\sqrt n}=93.43-2.708\times\frac{15}{\sqrt {40}}=87.01$
$Upper~bound=x ̅+t_{\frac{α}{2}}.\frac{s}{\sqrt n}=93.43+2.708\times\frac{15}{\sqrt {40}}=99.85$
