During off hours, cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute. The arrivals are distributed according to a Poisson distribution. What is the probability that during the next five minutes, three cars will arrive

Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

And the parameter represent the average ocurrence rate per unit of time

For this case we know that

And we want the probability that during the next five minutes, three cars will arrive, so then our rate becomes:

And we want this probability:

And if we use the pmf we got: