Thread: Very Famous but Tricky Poisson Problem

Hello, you all might have sees this problem before. Can anyone help? It would be great if anyone could show the procedures as well.

The number of oil tankers arriving at a certain refinery each day has a Poisson distribution with parameter λ = 2. Present port facilities can service three tankers a day. If more than three tankers arrive in a day, the tankers in excess of three must be sent to another port.
(a) On a given day, what is the probability of having to send tankers away?
(b) How much must present facilities be increased to permit handling all arriving tankers on approximately 90 percent of the days?
(c) What is the expected number of tankers arriving per day?
(d) What is the most probable number of tankers arriving daily?
(e) What is the expected number of tankers serviced daily?
(f) What is the expected number of tankers turned away daily?

Hey drinkingwater.

Can you show us what you have tried or thought about and any partial attempts? This is a standard type of problem in probability and no more unique than the others.