Dear J. Grabiner: On the Wolfram page which you quote, the topic is "normal numbers". This is quite an old bundle of concepts, discussed extensively, e.g., in the book "Uniform dustribution of sequences" by KUIPERS and NIEDERREITER. According to these authors, the concept dates back to some publications by Emile Borel, of 1909 and 1914. The concept is related to equal distribution on finite sets as well as to uniform distribution of real numbers modulo one. I learned about normal numbers from my teacher Edmund Hlawka who also treats them in his book on uniform distribution. I am not aware that any author treating normal numbers mentioned "normal distribution". Best regards, Peter Flor (Graz, Austria).