The number of oil tankers arriving at a refinery each day has a Poisson distribution with parameter . Current port facilities can service only four tankers a day so that if more than four tankers arrive in a day, the additional tankers must be sent to another port.
What is the expected number of tankers serviced daily at the current port facilities?
Is is simply ? The other information is extraneous?
I'd like to add on another part to the question. Suppose lambda is 1.5 and present port facilities can service three tankers a day. If more than 3 tankers arrive in a day, the tankers in excess of 3 must be sent to another port.
How much must present facilities be increased to permit handling all arriving tankers on approximately 90per cent of the days?
sorry i'm still stuck. i calculate poisson probability for i=0 + i=1 + i=2 + i=3 and already the cumulative probability is 0.9344. The current capacity of 3 tankers is already serving 90% of the tankers. The question asks how much must present facilities be increased so as to serve all the tankers 90% of the time...my calculation suggest that they do not need to increase facilities. Something is wrong...please could you help?