Computational problem and normal approximation
Evaluating the p-value for a hypothesis test about π using the binomial distribution can involve adding many binomial probabilities if the sample size, n, is large. Since binomial distributions are close in shape to normal distributions for large n, the normal distribution can be used to get an approximate p-value.
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Continuity correction (advanced)
Using a normal approximation to find the p-value for a test involves finding a z-score from the observed cound, x, then finding the probability from a standard normal distribution. A continuity correction improves the approximation by either adding or subtracting 0.5 from the observed count, x, before finding the z-score.
The continuity correction is most important when the observed count is near either 0 or n.