Question: Sam is a teaching assistant that also works the evening shifts in the library, being the only one on duty at the counter. Arrivals to

Sam is a teaching assistant that also works the evening shifts

Sam is a teaching assistant that also works the evening shifts in the library, being the only one on duty at the counter. Arrivals to the counter seem to follow a Poisson process with rate of 10 per hour. Each customer is served one at a time and the service time is thought to follow an exponential distribution with a mean of 4 min. (a) What is the probability that there are people waiting in line at any given time? (b) What is the average queue length? (c) How long does a customer spends in the system? (d) Sam has a pile of papers to grade, which they intend to do grade during their idle time at the library. If they can grade 22 papers per hour on average, how many papers per hour can they average while working their shift

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