Is it possible to obtain the sample min/max given the sample mean?

Question

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:

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

Answer 1

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.