Question 1051786
x====0====1====2====3
p(x)0.9=0.05 0.03==0.02
E(x), the mean is x*p(x)=0+0.05+0.06+0.06=0.17 defect per carton.
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variance is the average (here, a weighted average) of the squared deviations of the mean.  This is [x-E(x)]^2*p(x)

0.17^2*0.90=0.0260
0.83^2*0.05=0.0344
1.83^2*0.03=0.1098
2.83^2*0.02=0.1602
Sum is 0.3304 defective^2/box^2
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Standard deviation is sqrt(V(x))=0.5748 defective/box