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?

Re: Very Famous but Tricky Poisson Problem

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.