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 $0.238103.$