Normal Interval:
\begin{equation*}
P( 0.36 - 1.96 \sqrt{0.36 \cdot 0.64) / 400} \lt p \lt 0.36 + 1.96 \sqrt{0.36 \cdot 0.64) / 400}) = 1 - \alpha.
\end{equation*}
or
\begin{equation*}
P( 0.36 - 1.96 \cdot 0.6 \cdot 0.8) / 20 \lt p \lt 0.36 + 1.96 \cdot 0.6 \cdot 0.8) / 20) = 0.95
\end{equation*}
or
\begin{equation*}
P( 0.36 - 0.04704 \lt p \lt 0.36 + 0.04704) = 0.95 .
\end{equation*}
or
\begin{equation*}
P( 0.31296 \lt p \lt 0.40704) = 0.95 .
\end{equation*}
So, there is a 95% chance that the actual value for p lies inside the interval \((0.31296 , 0.40704).\)