Bank Wait Times

Suppose a small bank has one teller and customer transactions take 10 minutes on average. With 5.8 customers arriving per hour, what is the expected wait time? What would it be if you added a second teller?

With one teller, customers will wait nearly five hours on average. But adding a second teller makes the wait go down to 3 minutes.

Thanks to John D. Cook for this one.

Posted in Brain Teasers


4 Comments on "Bank Wait Times"

Greg says
March 17, 2023 @ 11:37

5.8 should be 58 minutes, 5 hours? Im perplexed

Doc says
March 17, 2023 @ 21:09

The answer seems incorrect to me. If 5.8 customers per hour take 10 minutes each then there is no wait time and the teller has 2 free minutes per hour assuming they arrive evenly spaced. Even if they all arrived at the top of the hour the last one served would only wait 48 minutes.

Mark W says
March 22, 2023 @ 01:42

The waiting time per customer, would depend on how often each one arrived, which was unspecified.
48 mins. waiting time, at the most; unless they all arrived at the start of the day?

5 Hrs on average?????????

I feel some vital details may be missing!

Riddler says
March 22, 2023 @ 03:59

I think more information is needed about the distribution of customer arrival times to answer this one.

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