Currently, you see 10 gates going in the East Entrance. On average, gate agents take 35 seconds to process a customer through the gate by scanning a QR Code. This processing time is exponentially distributed. Each gate has one gate agent, and each agent has his/her own line. You estimate that, on average, 50 fans arrive to the East Entrance (all 10 gates) every 3 minutes. The arrivals are exponentially distributed.

b. When looking at just one gate, how long (in minutes) do customers wait before arriving to the gate agent?

I know the answer should be 20.42min but i'm not sure how to get to that answer

c. How many fans, on average, are waiting to be serviced at one gate?

I know the answer should be 34.03 fans but I'm not sure how to get to that answer

Based on your BUAD 311 skills, you are convinced the fan experience would be better if you had one long, serpentine line supported by all gate agents (instead of a line for each agent). You would like to propose this change to The Coliseum Operations Manager, but you need to bring numbers to justify this proposal.

e) What is the new wait time in minutes if you have one long, serpentine line that is serviced by all gate agents? I know the answer should be 1.89 mins but I'm not sure how to get to that answer