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. 
A: Strictly speaking, the distribution is binomial.
But, Poisson approximation would also yield very similar results as n is large (Binomial tends to Poisson as n tends to infinity).
Even a Gaussian approximation would not be wrong (Central Limit Theorem).
A: As an illustration the following has the correct binomial distribution as blue $\circ$s, the very close Poisson approximation as red $+$s and the not quite so close Normal approximation (with continuity correction) as green $\times$s.

The Normal approximation fails to capture the slight right skewness, while it fails on both sides and the Poisson approximation fails on one side to capture the finite support.
