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Snicker · Answer 1 · 2023-04-24T01:41:19+0000

The mean formula is

$\mu=\Sigma x\cdot P(x)$

So, we have to multiply each number with each probability and then add them

$\begin{gathered} \mu=\Sigma x\cdot P(x) \\ \mu=0\cdot0.002+1\cdot0.034+2\cdot0.115+3\cdot0.212+4\cdot0.260+5\cdot0.225+6\cdot0.115+7\cdot0.031+8\cdot0.006 \\ \mu=4.02 \end{gathered}$

Then, we find the standard deviation-

$\begin{gathered} \sigma=\sqrt[]{\Sigma(x-\mu)^2P(x)}= \\ \sigma=\sqrt[]{(0-4.02)^2*0.002+(1-4.02)^2*0.034+(2-4.02)^2*0.115+(3-40.2)^2*0.212+(4-40.2)^2*0.260+(5-4.02)^2*0.225+(6-4.02)^2*0.115+(7-4.02)^2*0.031+(8-4.2)^2*0.006} \\ \sigma=\sqrt[]{635.93} \\ \sigma\approx25.2 \end{gathered}$ Hence, the mean is 4.02 and the standard deviation is 25.2

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