The mean formula is
[tex]\mu=\Sigma x\cdot P(x)[/tex]So, we have to multiply each number with each probability and then add them
[tex]\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}[/tex]Then, we find the standard deviation-
[tex]\begin{gathered} \sigma=\sqrt[]{\Sigma(x-\mu)^2P(x)}= \\ \sigma=\sqrt[]{(0-4.02)^2\times0.002+(1-4.02)^2\times0.034+(2-4.02)^2\times0.115+(3-40.2)^2\times0.212+(4-40.2)^2\times0.260+(5-4.02)^2\times0.225+(6-4.02)^2\times0.115+(7-4.02)^2\times0.031+(8-4.2)^2\times0.006} \\ \sigma=\sqrt[]{635.93} \\ \sigma\approx25.2 \end{gathered}[/tex]Hence, the mean is 4.02 and the standard deviation is 25.2