Q:

Binomial or Poisson ? Which one is correct for the following situation?

A large number of insects are expected to be attracted to a certain variety of rose plant.
A commercial insecticide is advertised as being $ 99 $%$ $ efective. Suppose $2000$ insects infest
a rose garden where the insecticide has been applied, and let $X$= number of surviving
insects.
What probability distribution might provide a reasonable model for this experiment?
My guess is it is a case of Binomial since $p=.99$ is very large .
But my friends opinions are it is Poisson distribution as  $n=2000$ is very large.
Which one is correct and why ?

A:

The natural model is binomial. Nowadays, computation is easy, so that is what one would use. 
In the old days, one might cross one's fingers and use a normal approximation. One can also note that the probability $p$ that a bug survives is given by $p=0.01$. So one could use the Poisson approximation to the binomial, with $\lambda=np=20$. The approximation is undoubtedly adequate, but most things one wants to calculate are still unpleasant to do by hand. 

