The normal approximation to the binomial distribution works best when the number of trials is large, and when the binomial distribution is symmetrical (like the normal distribution).

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The normal approximation to the binomial distribution is most accurate when the number of trials is large and the probability of success is not too close to 0 or 1. In addition, the shape of the binomial distribution does not necessarily have to be symmetrical for the normal approximation to work well.

The Normal Approximation to the Binomial Distribution Works Best When