In order to assume that the sampling distribution for a proportion is approximately normal,the population proportion must be very close to 0.50.

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Quizplus · Accepted Answer

The assumption of normality for the sampling distribution of a proportion is not based on the value of the population proportion itself. Rather, it depends on the sample size and the conditions of the binomial distribution being met. As a general rule, the normal approximation is appropriate if np≥10 and n(1-p)≥10, where n is the sample size and p is the population proportion.

In Order to Assume That the Sampling Distribution for a Proportion