On weekdays from 1130 to 200 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by the Poisson distribution. What is the probability that the vendor will have to wait at least 3 mintues for a customer?

Question

On weekdays from 1130 to 200 pm  customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by the Poisson distribution. What is the probability that the vendor will have to wait at least 3 mintues for a customer?

kropot72 · Answer

Average number of customers arriving in 3 minutes is:
$$\frac{25}{30}\times 3=2.5$$
$$P(X=x)=\frac{e ^{-\lambda}\lambda ^{x}}{x!}$$
$$P(X=0)=\frac{e ^{-2.5}2.5^{0}}{0!}=e ^{-2.5}$$