Analysis / Improbably High I.Q.

To illustrate exactly how improbable a given IQ score might be, see the following table of statistics on above average IQs. Scores are from the Stanford-Binet test, the original and best-known IQ test — see here. They follow a normal (bell curve) distribution with a mean of 100 points and a standard deviation of 15 points.

IQ Occurrence Frequency On Earth (of 7 500 000 000)
≥10050% 1 in              2 3 750 000 000
≥10537% 1 in              3 2 770 810 051
≥11025% 1 in              4 1 893 694 032
≥11516% 1 in              6 1 189 914 404
≥12009.1% 1 in             11 684 084 148
≥12504.8% 1 in             21 358 427 642
≥13002.3% 1 in             44 170 625 990
≥13500.98% 1 in            102 73 614 965
≥14000.38% 1 in            261 28 727 854
≥14500.13% 1 in            741 10 124 235
≥15000.043% 1 in          2 331 3 217 952
≥15500.012% 1 in          8 139 921 498
≥16000.003 2% 1 in         31 574 237 534
≥16500.000 73% 1 in        136 176 55 076
≥17000.000 15% 1 in        653 327 11 480
≥17500.000 029% 1 in      3 488 556 2 150
≥18000.000 004 8% 1 in     20 741 279 362
≥18500.000 000 73% 1 in    137 360 560 55
≥19000.000 000 099% 1 in  1 013 594 692 7
≥19500.000 000 012% 1 in  8 336 096 322 1
≥20000.000 000 001 3% 1 in 76 429 666 480 0
http://tvtropes.org/pmwiki/pmwiki.php/Analysis/ImprobablyHighIQ