# Poisson Distribution

• Mar 15th 2008, 10:58 AM
Niall2
Poisson Distribution
Hi I have a question:
The number of customers arriving at an office selling tickets for a festival can be modeled by Poisson distribution with mean 1.2 per 2 minute interval. Find the number of arrivals which will not be exceeded in at least 90% of 2 minute intervals.

I have an idea of how maybe I could answer it. Though it is a guess, so it may be way off:
Because
$P(X \leq 2; 1.2) = 0.879$
$P(X \leq 3; 1.2) = 0.966$
There will be no more than 3 arrivals in 90% of 2 minute intervals.

Also, as a second question, when I am told "A man sells 8 cars a week"
and am then told to calculate the probability of him selling "21 cars in two weeks", do I just modify the mean and then work out the probibility? i.e. find the the poisson probability $P(X = 21; 16)$
• Mar 15th 2008, 06:32 PM
mr fantastic
Quote:

Originally Posted by Niall2
Hi I have a question:
The number of customers arriving at an office selling tickets for a festival can be modeled by Poisson distribution with mean 1.2 per 2 minute interval. Find the number of arrivals which will not be exceeded in at least 90% of 2 minute intervals.

I have an idea of how maybe I could answer it. Though it is a guess, so it may be way off:
Because
$P(X \leq 2; 1.2) = 0.879$
$P(X \leq 3; 1.2) = 0.966$
There will be no more than 3 arrivals in 90% of 2 minute intervals.

Also, as a second question, when I am told "A man sells 8 cars a week"
and am then told to calculate the probability of him selling "21 cars in two weeks", do I just modify the mean and then work out the probibility? i.e. find the the poisson probability $P(X = 21; 16)$

Yes and yes.