Note from before that the Poisson distribution function was derived by approximating with Binomial and letting n approach infinity. Therefore, by the previous theorem, the Poisson variable is also approximately Normal using the Poisson mean and variance rather than the binomial’s. Indeed, in standard units
\begin{equation*}
\frac{Y - \mu}{\sqrt{\mu}}
\end{equation*}
is approximately normal for large \(\mu\text{.}\)