What distribution should I use for generating random client counts?

[twoflower]

Homework Statement

The bank is opened from 9:00 to 17:00. From 9:00 to 10:30 the average client count who come into bank is 32/hour, from 10:30 to 15:30 it is 26/hour and from 15:30 to 17:00 it is 50 clients per hour.

I have to test the hypothesis that the average count of clients who came to bank is 253 - this number was selected so that it's the sum of average counts for those time intervals.

I have to test this hypothesis based on sample of 250 days - I have to use random clients count $N_1, ..., N_{250}$. The problem is (for me) the way I must generate these random counts. They should be "drawn" from distribution, whose mean value is equal to average client count per day, ie. 253.

But what's the distribution like? I guess it's just some well known distribution and I must guess which one, but I can't find it out. I thought with exponential distribution I could do it, but it models rather intervals between events than count of the events itself. Then normal distribution came to my mind. It's quite appropriate I think but I don't know the variance it should have...

Thank you for any help.

 

[cepheid]

Homework Statement

I thought with exponential distribution I could do it, but it models rather intervals between events than count of the events itself.

...which would seem to be the job of the Poisson distribution, if I remember right. I'm not 100% sure though.

 

[twoflower]

...which would seem to be the job of the Poisson distribution, if I remember right. I'm not 100% sure though.

Thank you cepheid! That will be the one I'm looking for.