One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the probability of getting a specific value of a random variable is zero with the normal distribution.

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The normal distribution is a continuous probability distribution, which means that the probability of getting a specific value of a random variable is zero. In contrast, the binomial distribution is a discrete probability distribution, which means that the probability of getting a specific value is not zero. Therefore, when approximating the binomial distribution with a normal distribution, a correction for continuity adjustment is needed to account for this difference in probability calculation.

One of the Reasons That a Correction for Continuity Adjustment