Take a peek at the discussion at Should I continue to invest in an S&P 500 index fund?, in which I offer a look at the returns over shorter periods. The 20 yr returns are as follows
The total returns in the middle col, and CAGR last.
These are the returns for all 20 year periods from 1900-2014. It shows an average of 11%, and a minimum 3%. In other words, of 96 time periods, 51 were less than 10%, 45 were greater, and the average, 11.2%.
MoneyChimp offers S&P data easily copied into a spreadsheet. And you can manipulate to analyze as you wish.
The nature of returns is closer to a bell curve. You can't make that final assumption that you suggested. The disparity between getting less than 3X your money vs over 20X over the bad/good 20 year periods is what makes for difficulty planning strategies.
On a personal note - I am semi-retired. 53 yrs old. How different could I spend if I knew with certainty whether the next 40 years would return 3% vs 11%? (min, vs ave, I won't even fantasize over 15%+)