The sampling distribution for $\hat { p }$ is approximately normal for a large sample size $n$, where $n$ is considered large if both $n \hat { p } \geq 15$ and $n ( 1 - \hat { p } ) \geq 15$.

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Quizplus · Accepted Answer

The sampling distribution of $\hat{p}$ (the sample proportion) is approximately normal when the sample size is large enough that both $n\hat{p} \geq 15$ and $n(1 - \hat{p}) \geq 15$. This is a rule of thumb for ensuring that there are enough successes and failures for the Central Limit Theorem to apply, making the distribution of sample proportions approximately normal.

The Sampling Distribution For p^\hat { p }p^​ Is Approximately Normal for a Large Sample Size

The Sampling Distribution For $\hat { p }$ Is Approximately Normal for a Large Sample Size