# The mean number of oil tankers at a port city is 8 per day. The port has facilities to handle up to 12 oil tankers in day. What is the probability that too many tankers will arrive on a given day?

Assuming (perhaps without justification) a Poisson distribution,

the probability of more than 12 tankers arriving on a given day is (approximately)

If the tankers arrive with a Poisson distribution (which seems likely but not certain), then

The probability of

given the average of

is given by the formula:

and

the probability of

The probability of more than

These equations can be evaluated with a calculator or (as below) by using a spreadsheet:

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