How to Calculate Poisson Distribution Probabilities?

[mathsforumuser]

Hi guys I got a question on the poisson distribution and never previously done stats at all.

It follows:

The mean count of a radioactive substance is 25 disintegrations per minute. Using the Poisson distribution, find the probability that, in a time of 12 seconds, there are-

i) No disintegrations

ii) More than 2 disintegrations

 

[Jameson]

Hi mathsforumuser,

Welcome to MHB! :)

When working with any discrete probability distribution, we often need to use the probability mass function. For a Poisson distribution this is:

$$P[X=k]=\frac{\lambda^k e^{-\lambda}}{k!}$$

For this problem, what is $\lambda$? What is $k$?