# Estimation error from estimation quantile of normal distribution

• A
Hi guys,

For my (master) project I am trying to find the probability that a random variable, which is normally distributed, exceeds a quantile that is estimated by a limited number of observations. See attached for my attempt.
- Is it correct?
- How to incorporate the fact that the mean and variance of the normal distribution are unknown in reality?

#### Attachments

• Derivation_quantile.pdf
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mfb
Mentor
Why do you estimate it that way if you know your variable has a normal distribution? Find estimates of the mean and the standard deviation, calculate the quantile based on that. It will give you much better estimates especially for large deviations from the mean.

WWGD