I'm trying to figure out the formula to give back the value at percentile $p$ given that the values are normally distributed with mean $\mu$ and stddev $\sigma$.
If i recall correctly, the value is given by the inverse CDF function, but I was also wondering if given the sample size, how I might compute a confidence interval (say 95%) around the value assuming a sample size $n$.
I realise this question is similar to this one: What is the formula for a normal-theory confidence interval of the mean?, but that question doesn't have an accepted answer and has much back and forth in the comments.
Also in my case I'm not looking for a confidence interval around only the mean, but around any percentile.
