Spalding Doughnuts wants to know about its waiting line. Currently, Spalding Doughnuts uses a single-server, single-phase system when serving customers. Based on historical evidence, the average number of customers arriving per hour is 90 and is described by a Poisson distribution. They estimate that they can serve 120 customers per hour with the service times that follow an exponential distribution. Being that Spalding%u2019s customers have infinite patience and are willing wait in rain, sleet and snow for the chance to get the doughnuts of the gods, we do not see any balking or reneging. Being that Spalding Doughnuts is located in Lexington, Kentucky a city with a large population customers come from an infinite population. The Spalding family would like you to help them solve some thorny operational problems and figure out some system performance measures. Show the calculation please

a. On average, approximately how long do customers spend in the waiting line before they first get served?

b.What is the average number of customers waiting in line?

c.What is the probability of having more than 3 customers in the system?

d. What is the average utilization?

e. On average, approximately how long customers spend in the service system (i.e., the time from first getting in line until they receive their doughnuts)?