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The Economist magazine reports from a study of $\underline{20}$ subscribers that the average income is $\ 80,000$ USD with a standard deviation of the population is $\ 15,000$ USD. What's the real average income of all subscribers (the population) with $95 \%$ confidence?
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$\begin{gathered} P\left(\bar{x}-1.96\left(\frac{15000}{\sqrt{20}}\right) \leq \mu \leq \bar{x}+1.96\left(\frac{15000}{\sqrt{20}}\right)\right) \\ =+/-\ 6574.04 \end{gathered}$
So, with $95 \%$ confidence, the actual average income range for all subscribers would be between $\ 86,574$ and $\ 73,426$
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