Is it possible to obtain the sample min/max given the sample mean? Suppose we have iid $X_1, X_2, \dots, X_n$ samples of a standard normal distribution ($N(0, 1)$).

I am trying to get the sample minimum and the sample maximum, given that I know the value of n and the sample mean ($\bar{X}$). In summary, my goal is to obtain:


$E[\min(X_1, \dots, X_n)| \bar{X} = c ]$ for a known value of $c$
$E[\max(X_1, \dots, X_n)| \bar{X} = c ]$ for a known value of $c$


My first approach was using the expectation of the $k$-th order statistic $E[X_{(k)}]$, but I can't relate this expectation with the one I want to obtain.

Thanks
No.  Not even if you know the standard deviation.
For example:

-1.323, -.5, 0, .5, 1.323

Has a mean of zero and a sample standard deviation of close to 1

And:

-1.199,-.75,0,.75,1.199

Has a mean of zero and a sample standard deviation of close to 1

So starting with just the mean, sample size, and normal shape is not enough to restrict the data to just one possible max and min.
No.  Not even if you know the standard deviation.
For example:

-1.323, -.5, 0, .5, 1.323

Has a mean of zero and a sample standard deviation of close to 1

And:

-1.199,-.75,0,.75,1.199

Has a mean of zero and a sample standard deviation of close to 1

So starting with just the mean, sample size, and normal shape is not enough to restrict the data to just one possible max and min.