Question

It has been found that on average, four motorbikes go through an N1 tollgate every 20 minutes. What is the probability that

No more than 2 motorbikes will go through the tollgate in any randomly selected 20-minute period? Interpret your answer.

Answer 1

This is a Poisson distribution with the mean $\mu=4.$

$P(X\le2)=P(X=0)+P(X=1)+P(X=2)=e^{-4}(\frac{4^0}{0!}+\frac{4^1}{1!}+\frac{4^2}{2!})=$

$=0.0183+0.0733+0.1465=0.2381.$