A charity issues a large number of certificates each costing $£10$ and each being repayable one year after issue. Of these certificates, $1$% are randomly selected to receive a prize of £10 such that they are repaid as $£20$. The remaining $99$% are repaid at their face value of $£10$.
Consider a person who purchases $200$ of these certificates.
Use a Poisson approximation to this binomial distribution to approximate the probability that this person is repaid more than $£2,040$.
I know that $N$~$Bin(200,0,01)$ can be approximated to $Poi(2)$
So I've to calculate $P(S>2040)$, but I don't know how to proceed.
Hope someone can explain it to me. Thanks in advance.