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## Main Question or Discussion Point

Suppose you have a lavatory with 4 cubicles, in a company that has 30 employees using that lavatory.

Knowing that on average an employee spends 10 minutes in the cubicle, what is the probability that, at any given time, 0, 1, 2, 3 or 4 cubicles are in use? And what would be the average waiting time, if any?

I thought this would be a Poisson distribution situation, but then I'm not really sure it is the case, because if I'm not mistaken Poisson has no upper limit for the number of events, whereas here we can have at most 4 cubicles in use. And I thought with Poisson you needed to specify an interval of time: here I wouldn't know how to describe 'any given time'.

How would you go about tackling this?

Is this a known type of problem (I guess it would apply to supermarkets, post offices, etc...)?

Thanks!

L

Knowing that on average an employee spends 10 minutes in the cubicle, what is the probability that, at any given time, 0, 1, 2, 3 or 4 cubicles are in use? And what would be the average waiting time, if any?

I thought this would be a Poisson distribution situation, but then I'm not really sure it is the case, because if I'm not mistaken Poisson has no upper limit for the number of events, whereas here we can have at most 4 cubicles in use. And I thought with Poisson you needed to specify an interval of time: here I wouldn't know how to describe 'any given time'.

How would you go about tackling this?

Is this a known type of problem (I guess it would apply to supermarkets, post offices, etc...)?

Thanks!

L