Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as