We did a serological survey for a disease taking 300 samples in a population of 50 000.

If our sample mean gives a 2% prevalence. How do we work out the confidence intervals? I have all the formula's and there are great CI calculators on the web BUT seeing that is only one survey then does the central limit theorem apply allowing us to use the z-score from a normal distribution?

Or should we rathr use the z-score from a t-distribution?

Many thanks!

Johann