Z-interval

You use a z-interval when a normal curve models the sampling distribution of the statistic, which for a proportion requires a random sample, a population at least 10 times the sample, and at least 10 successes and 10 failures. The interval is $\hat{p} \pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where p-hat is the sample proportion and $z^*$ is the critical value. For example, with p-hat = 0.60 and n = 100, the standard error is $\sqrt{0.60(0.40)/100} = 0.0490$, so a 95% interval is $0.60 \pm 1.96(0.0490)$, or 0.504 to 0.696. For a mean you almost never know the population standard deviation, so you use a t-interval instead.