On New Year's Eve, during the night shift, emergency calls to paramedics arrive at a rate of three per hour. The director of operations can dispatch multiple vehicles during that time. The average time to make a trip and come back to base is 45 minutes. Arrival and service rates are both Poisson distributions. a. If the director wants the average time between a call made and an emergency vehicle dispatched not to exceed 20 minutes, how many vehicles should be scheduled for that night? b. If the number of vehicles scheduled is three, what proportion of the time are all emergency vehicles used? What is the probability that more than three calls will be in the system? c. If the number of vehicles scheduled is four, what proportion of the time are all emergency vehicles used? What is the probability that more than two calls will be in the system