Answer
$\mu = 0.17$
$ \sigma^2= 0.321$
$\sigma=0.567$
Work Step by Step
The data can be summarized as the following:
Probability 0.9, Number of defect 0
Probability 0.05, Number of defect 1
Probability 0.03, Number of defect 2
Probability 0.02, Number of defect 3
Use the formula to calculate the weighted mean as
$\mu = (0.9×0+0.05×1+0.03×2+0.02×3) / (0.9+0.05+0.03+0.02) = 0.17$
And use the formula to calculate the weighted variance as
$ \sigma^2= \frac{0.9×(0-0.17)²+0.05×(1-0.17)²+0.03×(2-0.17)²+0.02×(3-0.17)²}{0.9+0.05+0.03+0.02} = 0.321$
Standard deviation $\sigma=\sqrt {\sigma^2}=0.567$
