# Poisson Distribution with hourly rate

I have one question on probability,Which need the clear explanation

1. The number of customers appears at the ticket counter of PVR theatre at a rate of 120 per hour. Find the probability that during a given minute (i) No customer appear. (ii) At least two customers appear.

Please Say whether it comes under the poisson, if so what would be the mean value.

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Yes, it looks like you might be expected to use the Poisson distribution here, perhaps with a rate measured in customers per minute. Can you figure out the arrival rate in customers per minute from the given information? – Dilip Sarwate Nov 26 '12 at 12:53
@ Dilip Sarwate Thanks for commenting, This much only the data is available for this. any way to solve it – Exhausted Nov 26 '12 at 12:57
If customers arrive at the ticket counter at an average rate of 120 per minute, what would you say the average rate of arrivals per minute? – Dilip Sarwate Nov 26 '12 at 13:04

## 1 Answer

If a distribution has the property that the probability does not depend on any previous values, and is a rate, then Poisson is probably a good way to model it. In this case, that seems relatively fair - people are not less likely to show up if there are fewer or more people that showed up in the past.

The parameter you need depends on the rate. The rate is given as 120/hour. If you want the rate per minute, you can simply divide by 60, since the distribution can scale to any given time scale.

The mean value is simply the expected number of people, 120 in any given hour, or 2 per minute. To turn this into the Poisson distribution, we use the fact that the rate is the same as the distribution parameter. You can then evaluate the Poisson distribution to find the answer to your question.

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Thanks for your valuable suggestion. I will refer and accept your answer. – Exhausted Nov 27 '12 at 5:29