The random variable Y, the number of cars that arrive at an intersection during a specified period of time, often possesses (approximately) a Poisson probability distribution. When the mean arrival rate l is known, the Poisson probability distribution can be used to aid a traffic engineer in the design of a traffic control system. Suppose you estimate that the mean number of arrivals per minute at the intersection is one car per minute.
a. What is the probability that in a given minute, the number of arrivals will equal three or more?
b. Can you assure the engineer that the number of arrivals will rarely exceed three per minute?