Nope, not buying it. I don’t know if the formula they talk about is valid or not, but if it is, they are misapplying it.
From the explanation @linsalt posted:
“The waiting times given above assume the model has approached its steady state. That is, the bank has been open long enough for the line to reach a sort of equilibrium.”
That assumption takes it out of the real world, because the vast majority of banks are not open infinite hours.
Most banks are open 9 hours a day at most. At 5.8 customers/hour, that’s 52.2 customers per day. Let’s call it 53 to simplify it.
Let’s assume the worst possible scenario. All 53 customers arrive at the EXACT same moment. Customer 1 waits 0 minutes. Customer 2 waits about 10 minutes. Customer 3 waits about 20 minutes. All the way up to poor Customer 53, who waits all 520 minutes. (Assuming the poor teller sticks around.)
The total wait time for all 53 customers combined is 13,780 minutes. The average wait time is 260 minutes, or 4.3 hours. If any customers arrive at different times (highly likely), it goes down from there.
The bank has to be open over 10.5 hours AND all of the customers still have to arrive at the exact same time to get the average wait up to 5 hours.
P.S. I noticed that using the formula it’s actually 4.83 hours (the original problem says almost 5 hours). That’s still a bank open for over 10 hours with all the customers arriving at the exact same time.