Suppose that cars arrive at a toll booth according to a Poisson process with intensity 5 per minute. What is the probability that no cars will arrive in a particular minute? What is the probability that more than 8 cars will arrive in a particular minute? What is the probability that exactly 9 cars will arrive in a given two minute period, and what is the expected number of arrivals during that period? Comment on the applicability of the assumptions of the Poisson process for this example.