PROBLEM $2$

Suppose vehicles arrive at a signalized road intersection at an average rate of $240$ per hour and that the cycle of the traffic light is set at $45$ seconds. What is the probability that the number of vehicles arriving at the signal during that cycle will be $($a$)$ exactly $5,($b$)$ fewer than $5,($c$)0,$ and $($d$)$ more than $3?$