Question

The number of people arriving for treatment at an emergency room can be modelled by a Poisson process with a mean of five people per hour.

(a) What is the probability that exactly four arrivals occur at a particular hour?

(b) What is the probability that at least four people arrive during a particular hour?

(c) How many people do you expect to arrive during a 45-min period?

Answer 1

(a) $P(X=4)=e^{-5}\frac{5^4}{4!}=0.1755.$

(b) $P(X\ge 4)=1-P(X<4)=1-e^{-5}(\frac{5^0}{0!}+\frac{5^1}{1!}+\frac{5^2}{2!}+\frac{5^3}{3!})=0.7350.$

(c) $\mu=E(X)=5\frac{45}{60}=3.75.$