We have $$ S = \sum _{k=1} ^{n} X_{k}$$ each $X_k$~$ Poisson(1)$. I want to find $$P\{S_{100} \ge200\}$$
I first approximate $S_{100}$ to standard normal.
$$P\{\frac{S_{100} - 100}{\sqrt{100}} \ge \frac{200 - 100}{\sqrt{1} \cdot \sqrt{100}}\}$$
Which result in $$ P\{Z \ge 10\}$$
Then I find it difficult to process it...
This probability is actually (EDIT) $\approx 0$. There is no need to use tables or calculators; just observe that the range of a Standard gaussian is for 99.99% in $[-3.8;3.8]$