Question

A study of corruption for a certain geographic region showed an average of 5 corruptions occur per 20,000 people. In a city of 80,000 people, find the probability that at least 3 corruptions occur.

Answer 1

Poisson distribution

$\lambda=5×4=20$

$Px\ge3)=1-P(x\le2)$

$=1-(\frac{\lambda^xe^{-\lambda}}{x!}),x=0,1,2$

$=1-(\frac{20^0e^{-20}}{0!}+\frac{20^1e^{-20}}{1!}+\frac{20^2e^{-20}}{2!})$

$=1-(221e^{-20})$

$=0.9999999979$