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At a Lebanese bank in downtown Beirut, people arrive randomly at a bank teller at an...

At a Lebanese bank in downtown Beirut, people arrive randomly at a bank teller at an average rate of 30 an hour. If the teller takes an average of 0.5 minutes to serve each customer, what is the average number of customers in the queue and how long do they wait to be served?
Q2.1 What happens if the average service time increases to 1 minute?
Q2.2 What happens if the average service time increases to 2 minutes?

Math   Statistics-And-Probability   
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Answer #1

Dear student, please comment in the case of any doubt and I would love to clarify it.

Suppose there are just 30 customers in an hour for the teller machine(mentioned in the question) and the teller takes 0.5 minutes to serve each customer.

It will take (0.5*30) minutes, which is 15 minutes for the teller to deal with every customer, the last person in the queue has to wait for 14.5 minutes whereas the second customer has to wait for 0.5 minutes.

The average number of customers will be 30 at any point in time.

2.1)

If the average service time increases to 1 minute, then the last person in the queue has to wait for 29 minutes whereas the second customer has to wait for 1 minute.

2.2)

If the average service time increases to 2 minutes, then the last person in the queue has to wait for 58 minutes whereas the second customer has to wait for 2 minutes.

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