Binomial becomes normal as \(n \rightarrow \infty\text{.}\) Consider n = 50 and p = 0.3. Then, \(\mu = 15\) and \(\sigma^2 = 10.5\text{.}\)

Using the binomial formulas, for example,

\begin{equation*} P( X = 16 ) = \binom{50}{16} 0.3^{16} \cdot 0.7^{34} \approx 0.11470 \end{equation*}

Using the normal distribution,

\begin{align*} P( X = 16 ) & = P( 15.5 \lt X \lt 16.5) \\ & \approx normalcdf(15.5,16.5,15,sqrt(10.5)) \\ & = 0.11697 \end{align*}

Notice that these are very close.