For the sampling distribution of the proportion (p-bar) to follow a normal distribution, certain conditions need to be met. Specifically, the sample size should be sufficiently large, and the sample proportion should not be too close to 0 or 1. A common rule of thumb is that both np and n(1-p) should be greater than or equal to 10, where n is the sample size and p is the true proportion of success. This ensures that there are enough successes and failures in the sample to approximate a normal distribution.
In simpler terms, when you take a random sample, if you want to be confident that the distribution of the sample proportion looks like a bell curve (normal distribution), you need to make sure that your sample is big enough and that the proportion of successes is not extreme. If these conditions are met, then we can apply the normal approximation to conduct hypothesis tests or create confidence intervals for the population proportion.