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?
1 Answer
Assuming (perhaps without justification) a Poisson distribution,
the probability of more than 12 tankers arriving on a given day is (approximately)
Explanation:
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: