I need to estimate 90th percentile of a normal distribution. Assuming that I have a small sample(<30) of the population of this distribution how can I estimate the 90th percentile? what assumptions can I make regarding the distribution of the sample. I think CLT is not applicable here because I dont want any CI for the mean. Note that the standard deviation of the population is unknown.
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Another term for estimates of percentiles--especially when it is desired to provide a confidence limit for the estimate--is [*tolerance limit*.](https://stats.stackexchange.com/questions/44743/tolerance-bound-for-a-normalized-variable/47326#47326). One answer in the duplicate answers your question and another answer explains how to obtain tolerance limits for Normal distributions. – whuber Feb 02 '18 at 14:41