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The Indiana State Police wish to estimate the average mph being traveled on the Interstate Highways, which cross the state. If the estimate is to be within $\pm 5$ mph of the true mean with $95 \%$ confidence and the estimated population standard deviation is $25 \mathrm{mph}$, how large a sample size must be taken?
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\begin{aligned}
&\text { 95% CI: } \bar{x} \pm z^{*} \cdot \sigma / \sqrt{n} \\
&\text { margin of error }=z^{*} \cdot \sigma / \sqrt{n} \\
&5=1.96 \times 25 / \sqrt{n} \\
5=(1.96 \times 5)^{2} &=96.04 \\
& \approx 97
\end{aligned}
\end{aligned}
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