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Feb 19, 2023 at 23:01 comment added Alex J Tbh I'd probably just try a bootstrap method.
Feb 18, 2023 at 23:26 comment added jginestet Thanks for the answer. As you indicated, this is the "basic" answer; just look it up in a Z table, and I would have my answer. But then all I get a a point estimate ̂p of that proportion (just like I got a point estimate of the mean and sd). What I am really after is the "confidence interval" of the proportion, e.g. there is 95% confidence that we will find between p1 and p2 inside (LL, UL). And indeed p1 and p2 will take into account the uncertainties on μ^ and σ^. I have not found any source on this...
Feb 18, 2023 at 23:20 comment added jginestet Thanks for the answer. As you indicated, this is the "basic" answer; just look it up in a Z table, and I would have my answer. But then all I get a a point estimate of that proportion (just like I got a point estimate of the mean and sd).
Feb 16, 2023 at 3:57 history answered Alex J CC BY-SA 4.0