Now is a perfect time for people to bone up on the rabbit hole that is binomial confidence intervals! https://en.wikipedia.org/wiki/Binomial_proportion_confide

Now is a perfect time for people to bone up on the rabbit hole that is binomial confidence intervals! https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval https://en.wikipedia.org/wiki/Binomial_proportion_confidence... TLDR: whether you're a frequentist or Bayesian, the Jeffrey's interval is pretty good. Use Clopper-Pearson if you're a frequentist who is scared of undercovering. I get 0.011% for the 2.5% quantile and 0.46% for the 97.5th quantile.