How does the alpha brain wave frequency range distribute over the population? Alpha brain waves show up in your EEG when you close your eyes. Alpha waves are brain waves between 8 and 13 Hz.

How does this frequency range distribute over a population of people?
Alpha oscillations vary in frequency within a single subject from brain area to brain area (Başar, 2012),  likely because there is not a single phenomenon underlying all examples of alpha oscillations.  At this point in time, an answer to this question would be very difficult because we don't even know what alpha oscillations are.

Reference

Başar, E. (2012). A review of alpha activity in integrative brain function: fundamental physiology, sensory coding, cognition and pathology. International Journal of Psychophysiology, 86(1), 1-24.