Answer to Question #254979 in Statistics and Probability for zeee

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 $\mu=4.$

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

$=0.0183+0.0733+0.1465=0.2381.$