Answer to Question #255122 in Statistics and Probability for Zah

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

Let $X=$ the number of motorbikes through the tollgate: $X\sim Po(\lambda t)$

Given $\lambda t=4.$

$$P(X\leq 2)=P(X=0)+P(X=1)+P(X=2)$$

$$=\dfrac{e^{-4}\cdot4^0}{0!}+\dfrac{e^{-4}\cdot4^1}{1!}+\dfrac{e^{-4}\cdot4^2}{2!}=13e^{-4}$$

$$\approx0.238103$$

The probability that no more than 2 motorbikes will go through the tollgate in any randomly selected 20-minute period is $0.238103.$