Question

A typical sheet of metal has on the average 2 defects per 5 m^2. What is the probability that a 10 m^2 sheet of metal will have at least 3 defects?

Answer 1

If a Poisson distribution has been assumed, then

$\lambda$ (average number of defects) in "x" square meters

2.0 5.0

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda$ 10.0

$$\lambda={2.0\times 10.0\over 5.0}=4.0$$

$$P(X\geq3)=1-P(X\leq2)=1-[P(X=0)-P(X=1)-P(X=2)]=$$

$$=1-{e^{-4}\times4^0 \over 0!}--{e^{-4}\times4^1 \over 1!}--{e^{-4}\times4^2 \over 2!}=$$

$$=1-13e^{-4}\approx0.7619$$