Answer to Question #325880 in Statistics and Probability for Mester

Question

The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 2.5 work-related injuries a month. What is the probability that in a given month, no work-related injuries occur? That at least one work-related injury occurs?

Answer 1

We have a Poisson distribution,

$\lambda=2.5;\\ P_t(X=k)=\cfrac{(\lambda t)^k\cdot e^{-\lambda t}}{k!}.$

$1) P_{1}(X=0)=\cfrac{(2.5\cdot1)^0\cdot e^{-2.7\cdot1}}{0!}=0.0821;\\ 2) P_{1}(X\ge1)=1-P(X<1)=1-P(X=0)=\\ =1-0.0821=0.9179.$