Question

From past experience, a company has found that in a box of four triple A batteries, 74% contain no defective battery, 7% contain one defective battery, 4% contain two defective batteries, 6% contain three defective batteries, and 9% contain all defective batteries. Calculate the mean, variance, and standard deviation for the defective batteries.

Answer 1

$\mu =\Sigma xp(x)=0*0.74+1*0.07+2*0.04+3*0.06+4*0.09=0.69.$

$\sigma ^2=\Sigma x^2p(x)-\mu ^2=0*0.74+1*0.07+4*0.04+9*0.06+16*0.09-0.69^2=1.7339.$

$\sigma =\sqrt{\sigma ^2}=\sqrt{1.7339}=1.3168.$