# Math Help - Poisson Distribution Help

1. ## Poisson Distribution Help

Ok, here's the problem.

The Number of medical emergency calls per hour has a Poisson distribution with parameter $lambda$. A record of emergency calls is available for a sufficient amount of time and parameter $lambda$ is assumed to be the same throughout the available recording of calls. Number of emergency calls at different hours are independant. If $lambda$ equals 1, what is the probability of at least 20 emergency calls in the 10 consecutive hours of a single medical response team shift??

I think I must be using the wrong formula, or just approaching this problem incorrectly. My probablities keep coming out in varieties of 1.9 to the negative 60th, etc. I really don't think that answer is correct.

Help please?

2. Originally Posted by ScienceGeniusGirl
Ok, here's the problem.

The Number of medical emergency calls per hour has a Poisson distribution with parameter $lambda$. A record of emergency calls is available for a sufficient amount of time and parameter $lambda$ is assumed to be the same throughout the available recording of calls. Number of emergency calls at different hours are independant. If $lambda$ equals 1, what is the probability of at least 20 emergency calls in the 10 consecutive hours of a single medical response team shift??

I think I must be using the wrong formula, or just approaching this problem incorrectly. My probablities keep coming out in varieties of 1.9 to the negative 60th, etc. I really don't think that answer is correct.

Help please?
The number of calls over a ten hour period follows a Poisson distribution with a mean of (10)(1) = 10.

Calculate $\Pr(X \geq 20) = 1 - \Pr(X \leq 19)$.

I get 0.9965.

3. Ohh, that makes a lot more sense

Thank you!