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

$\displaystyle P(X \leq 2; 1.2) = 0.879$

$\displaystyle P(X \leq 3; 1.2) = 0.966$

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 $\displaystyle P(X = 21; 16)$