Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables from a distribution having mean $\mu$ and variance $\sigma^{2}$. From the central limit theorem, \begin{align} \frac{X_{1} + X_{2} + \cdots + X_{n} - n\mu}{\sigma \sqrt{n}} \sim \mathcal{N}(0, 1) \end{align} or, the sum of the random variables follows the distribution of a standard normal as the value of $n$ becomes large. Typically, the property starts to manifest as soon as $n$ becomes around 30.