Answer to Question #157585 in Statistics and Probability for Shanker

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? What is the probability that atleast one work-related injury occurs?

Answer 1

$P(x=0)=\frac{e^{-2.5}2.5^{0}}{0!}\approx 0.082\\ P(x\geq 1)=1-P(x=0)\\ =1-\frac{e^{-2.5}2.5^{0}}{0!}=0.918$