1. ## Poisson distribution

Hi

I need help setting this up.

Grasshoppers are distributed at random in a large field according to a Poisson distribution with parameter alpha = 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals .99?

I think the problem I'm having is with the square yard and radius. I know that to calculate pr(x =>1) = 1 - pr(x = 0).

2. Originally Posted by shogunhd
Hi

I need help setting this up.

Grasshoppers are distributed at random in a large field according to a Poisson distribution with parameter alpha = 2 per square yard. How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals .99?

I think the problem I'm having is with the square yard and radius. I know that to calculate pr(x =>1) = 1 - pr(x = 0).
Let the radius of the sampling region be $\displaystyle r$ yards, then the area of the sampling region is $\displaystyle \pi r^2$, and the mean number of grasshoppers in the sampling region is $\displaystyle 2 \pi r^2$.

RonL