Math — Normal Approximation
Approximating the binomial by a normal distribution.
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X \sim B(n,p) \approx N\big(np,\ np(1-p)\big)
\text{continuity correction } \pm 0.5
Z = \frac{X - \mu}{\sigma}
\text{valid when } np > 5 \text{ and } n(1-p) > 5