Answer to Question #210485 in Statistics and Probability for Vickie

Question

Truck driver at the border tool station to be cleared at a rate of two per hour the distribution of arrivals approximates a poisson distribution

What is the probability that no truck arrives in a particular hour

What is the probability that at least one truck arrives during a particular hour

Answer 1

Let $X=$ the number of tracks arrived: $X\sim Po(\lambda).$

Given $\lambda=2$

$$P(X=0)=\dfrac{e^{-2}\cdot2^0}{0!}=e^{-2}\approx0.135335$$

$$P(X\geq 1)=1-P(X=0)=1-\dfrac{e^{-2}\cdot2^0}{0!}$$

$$=1-e^{-2}\approx0.864665$$