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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?

Thanks in advance!

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?

Thanks in advance!