Answer to Question #125327 in Statistics and Probability for Hagan

Question

A Covid 19 testing machine at a testing centre breaks down an average of three times per year. Using an appropriate probability distribution formula, find the probability that during the next year, this machine will have;

i. exactly two breakdowns

ii. at most one breakdown

Answer 1

This is a Poisson distribution with $\lambda=3.$

$P(X=k)=e^{-\lambda}\frac{\lambda^k}{k!}$

i. $P(X=2)=e^{-3}\frac{3^2}{2!}=0.2240.$

ii. $P(X\le1)=P(X=0)+P(X=1)=e^{-3}\frac{3^0}{0!}+e^{-3}\frac{3^1}{1!}=0.1991.$