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I'm working on a probability question with mean and variance.

Let's say that I have two banks. They are identical in every way, except that bank A has five lines with ten people each and bank B has one line with fifty people. There are five tells in each bank.

In bank A, each of those tellers is dedicated to serving one line and in bank B, the teller serves the next available customer. Which has a faster average wait time and longer variance wait time?

I understand the first part of the question. The average wait time is the same because it is, in your line, the time to help each customer * the number of customers / the number of bank tellers.

For bank A, that's time * 10 / 1 and for bank B, it's time * 50 / 5.

I don't understand the second part of the question though. Intuitively, I think that bank B should have a longer standard deviation for wait time since there are more people and you have a greater chance at getting extreme outliers, or customers who take much longer than anyone else.

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    $\begingroup$ i think what the question implies re bank A is "five lines with ten people each". So the population sizes are equal. Otherwise the question does not make much sense. $\endgroup$
    – Zhubarb
    Commented Jun 3, 2019 at 14:36
  • $\begingroup$ here's an answer: math.stackexchange.com/questions/2117151/… $\endgroup$
    – Edgar
    Commented Jun 3, 2019 at 14:50
  • $\begingroup$ @Zhubarb, thank you. I updated for clarity. $\endgroup$
    – ivan
    Commented Jun 3, 2019 at 14:52
  • $\begingroup$ @Edgar, the poster said it's easy to demonstrate the difference in variability between the two lines but I still don't see it. $\endgroup$
    – ivan
    Commented Jun 3, 2019 at 14:52
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    $\begingroup$ There's also this - eventuallyalmosteverywhere.wordpress.com/2012/04/10/… $\endgroup$
    – ivan
    Commented Jun 3, 2019 at 15:00

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