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Given a normally distributed data.

And the population mean $\mu$

I want to find estimate the mean of any arbitrary interval $[a,b]$ using the population mean $\mu$, i know it can be done easily using some integrals, however I want to know if the normal distribution have any special properties related to that.

Perhaps the midpoint of the interval is the mean of the interval?

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  • $\begingroup$ The midpoint of the interval is the mean of the interval only when the interval is symmetric about $\mu$. $\endgroup$
    – Henry
    Commented Aug 5 at 11:05

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You might check the properties of the truncated normal distribution. Knowing the mean and truncation interval is not sufficient. The variance of the normal distribution is also needed.

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