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For the following question, I've determined the mean to be \$0.20, but how do I determine the standard deviation?

A slot machine at a casino pays out an average of \$0.9, with a standard deviation of \$120. It costs a dollar per play. If a person plays 2 times, what are the mean and standard deviation of the casino's profit?

I've calculated the variance to be $\$120^2=\$14400$, and then $(\$14400)(2^2)=57600$ (since the person played twice), taking square root: SD=$\sqrt{57600}=\$240$.

But in fact, the SD= $\$169.71$.

Why?

Update: I now realize that each event is independent and that I should add the variances instead of multiply.

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Why do you multiply the variances? You have to sum them up!

$SD = \sqrt{120^{2} + 120^{2}} = \sqrt{28,800} = 169.7056$

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