(Covid Inoculation) At some point in the future, a single nurse is inoculating children against Covid-19 at a local clinic. An average of 12 children per hour is expected to arrive according to a Poisson process. She serves the children at a rate of 15 per hour. Assume that the service time distribution is approximately exponential. What is the utilization of the nurse? What is the average time spent by a child in the system (i.e. time spent waiting in line and time spent being vaccinated)? What is the average number of children in the system? What is the average number of children in line? How long on average does a child spend waiting in line?