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meymathis · #2 December 17th, 2008, 02:26 PM

I will use the formulation of Poisson from wikipedia.

$\lambda$ is the expected number of occurrences over the particular interval of interest. So in our case the expected rate of occurrence is $15/30=0.5$ cars per minute. So the expected number of cars in 36.78 minutes is: $\lambda=15/30*36.78=18.4$

If $N$ is the number of cars that arrive in 36.78 minutes, then the question can be rephrased to: what is the probability that $N<11$

The PDF is:
$f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!}$

So

$\mathrm{P}(N<11) = \sum_{k=0}^{10}\frac{\lambda^k e^{-\lambda}}{k!}=\ldots$