Sampling distribution of the sample proportion

Collect $\hat{p}$ (p-hat, the sample proportion) from every possible sample of size $n$ and you have its sampling distribution, centered on the population proportion: $\mu_{\hat{p}} = p$. Its spread is $\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$ (the square root of p times one minus p, all over n). With $p = 0.6$ and $n = 150$, that is $\sqrt{\frac{0.6(0.4)}{150}} = \sqrt{0.0016} = 0.04$. The shape is close to normal when $np \ge 10$ and $n(1-p) \ge 10$, which holds here because $np = 90$ and $n(1-p) = 60$.