From rmg3@access2.digex.net Sun Sep  6 13:52:32 EDT 1998

  The question comes up often enough that I devoted a few brain cells
to it while driving on vacation.  Here's an approach:

  The standard of 12 minutes for 1.5 miles was advanced as a standard of
fitness by Cooper (right?).  I believe (corrections please) this was
meant as a time that almost any (male?) could meet with some practice. 
I'll guesstimate 'almost any' as being 95% of the population.

  On the other hand, certainly the fastest anyone runs 1.5 miles is
about 6 minutes.  Call that faster than all but 1 in a million.

  Now, if we guess the distribution of running paces for 1.5 miles as
being a bell curve (and I've got no evidence that it is) we can procede
a little more.  The 12 minute 1.5 mile is at +1.6 standard deviations.
The 6 minute guys are at ... call it -4.4 standard deviations.  (My tables
don't go out to 6 decimal places.  I've taken 4.4 as a guess, and one
which makes the next parts come out even.)

  The standard deviation is then 1 minute, and the mean is 10.4 (10:24).
For complete roundness, call it 1 minute standard deviation and 10:30 mean.
Given that, a loose look at the table is:
10:30  50 percentile
10:00  69      (faster than all but 3 in 10)
 9:30  84      (faster than all but 1 in 6)
 9:00  93      ( "" 1 in 14)
 8:30  97.7    ( "" 1 in 40)
 8:00  99.4    ( "" 1 in 170)
 7:30  99.9
 
  These numbers are vaguely reasonable for my memory of high school running
among the boys.  

  Given the number of times I said 'guess' above, certainly none of this
should be taken particularly seriously.  I'm almost positive that the 
distribution of running times is not a bell curve (long tail towards the
fast side with a lot of bunching on the slower side is my expectation).
And there are no adjustments for age, sex, training, ...

  And, more importantly, there's no consideration of the fact that umpteen
percent of the population doesn't run period, so that the 20 minute 1.5 milers
are still, in fact, doing quite well compared to most of the population.

-- 
Robert Grumbine rmg3@access.digex.net http://www.access.digex.net/~rmg3/
Sagredo (Galileo Galilei) "You present these recondite matters with too much 
evidence and ease; this great facility makes them less appreciated than they 
would be had they been presented in a more abstruse manner." Two New Sciences