Problem: Kasser Theater at Montclair State University is looking to streamline their ticket check as patrons are entering the theater. Since the majority of the ticket holders purchase their tickets online and can easily show the QR code for the event, only one employee is needed to scan each ticket. S/he is able to scan an average of 8 tickets per minute. Before the show starts, audience members arrive at a 5 per minute. Assume arrivals follow the Poisson distribution and service times follow the exponential distribution.
1. What is the average number of patrons waiting in line?
2. What is the average time a patrons spends in the waiting line?
3. What is the average number of patrons in the system?
4. What is a patron's average time in the system?
5. What is the probability that someone is being processed when a patron arrives?