Question

A manufacturer knows that the condensers he makes contain an average 1% effective. He packs them in boxes of 100. The probability that a box picked at random will contain 3 or more faulty condensers________(Correct upto 3 decimal places)

• A. 0.0803

Answer 1

The correct option is A 0.0803
P = Probability of defective condensers
= 1% = 0.01
n = Total number of condensers = 100
$\therefore$ $\lambda$ = mean = nP = 100(0.01) = 1

From Poisson distribution,

$P(X=x)=P\left(x\right)=\frac{e^{-\lambda }.{\lambda }^x}{x!}=\frac{e^{-1}{.1}^x}{x!}=\frac{e^{-1}}{x!}$


$P(x\ge 3)=1-P(x<3)$

$=1-[e^{-1}+e^{-1}+\frac{e^{-1}}{2}]$

$=1-e^{-1}.\frac{5}{2}=1-0.9197=0.0803$