Question

A certain kind of sheet metal has, on average, 9 defects per 20 square feet.

Assuming a Poisson distribution, find the probability that a 32 square foot metal sheet has at least 18 defects. Round your answer to four decimals.

Answer 1

There are on average $\lambda=9*\frac{32}{20}=14.4$ defects per 32 square feet.

$P(X\ge18)=1-P(X<18)=1-e^{-\lambda}\sum_{i=0}^{17}\frac{\lambda^i}{i!}=$

$=1-e^{-14.4}\sum_{i=0}^{17}\frac{14.4^i}{i!}=1-0.7975=0.2025.$