For random variables
\begin{equation*}
W_n = \frac{\overline{X} - \mu}{\sigma/ \sqrt{n}}
\end{equation*}
with corresponding distribution function \(F_n(W_n)\text{,}\)
\begin{equation*}
\lim_{n \rightarrow \infty} F_n(c) = \int_{-\infty}^c \frac{1}{\sqrt{2 \pi}} e^{-z^2/2} dz = \Phi(c)
\end{equation*}
that is, the standard normal distribution function.