The no. of trees for an acre is a poisson random variable with mean 30. Find the probability that the no. of trees for 35 acres is at least 31?
How do I go about gathering this. I know i can get such a distribution for 1 acre via just inserting the values into the poisson distribution function, but what do you do for 35?
The number of trees in 35 acres is also Poisson but with mean $35 \cdot 30$.
This fact can be justified either by the assumptions of a Poisson scatter or by noting that the sum of $n$ independent $\text{Poisson}(\lambda)$ random variables is $\text{Poisson}(n\lambda)$.