Davin: the chice of using mu versus xbar was deliberate, as they represent different quantities: the population mean versus a sample mean. But reading over the docs with fresh eyes, I can now see that the distinction is not as clear as I intended.

I think that changing the names now would be a breaking change, but even if it wasn't, I don't want to change the names. The distinction between population parameters (mu) and sample statistics (xbar) is important and I think the function parameters should reflect that.

As for the new NormalDist class, we aren't limited by backwards compatibility, but I would still argue for the current names mu and sigma. As well as matching the population parameters of the distribution, they also matches the names used in calculators such as the TI Nspire and Casio Classpad (two very popular CAS calculators used by secondary school students).

See #36099. If you would like to suggest some doc changes, please feel free to do so.