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Does the standard error (SE) estimate of the mean (SE = sigma/sqrt(n)) only apply to the mean, or can it be applied to any value in the fit normal distribution?

For example, if estimated 95th percentile of the fit normal distribution is 10, and the SE is 2, would the 95% confidence intervals on the 95th percentile estimate be 10 +/- 1.96*2?

I have thus far been using the binomial quantile confidence interval method to get a probability of exceedance and then plugging that back into a inverse normal function, but some of my results seem odd.

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    $\begingroup$ Could you provide the specifics of how a normal distribution was fit to the data? Ordinarily it's done using estimates of the mean and variance, but which estimates exactly? And is this supposition correct or did you use a different technique, such as regression of a probability plot or estimates of specific percentiles? $\endgroup$
    – whuber
    Aug 10, 2016 at 14:33
  • $\begingroup$ Thank you for the response, by "fit" I only mean that I took 8 samples and determined the arithmetic mean and population standard deviation. I would then like to assume a normal distribution (I know the data is normal) and use the mean and std to estimate the 95th percentile and I want to know how to calculate a confidence interval for the percentile estimate. $\endgroup$
    – rconway91
    Aug 10, 2016 at 14:38
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    $\begingroup$ OK, good. It might help to know that confidence limits for percentiles are called tolerance limits. $\endgroup$
    – whuber
    Aug 10, 2016 at 14:40

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