<P> Because of the exponential tails of the normal distribution, odds of higher deviations decrease very quickly . From the rules for normally distributed data for a daily event: </P> <Table> <Tr> <Th> Range </Th> <Th> Expected fraction of population inside range </Th> <Th> Approximate expected frequency outside range </Th> <Th> Approximate frequency for daily event </Th> </Tr> <Tr> <Td> μ ± 0.5 σ </Td> <Td> 0.382 924 922 548 026 </Td> <Td> 2 in 3 </Td> <Td> Four times a week </Td> </Tr> <Tr> <Td> μ ± σ </Td> <Td> 0.682 689 492 137 086 </Td> <Td> 1 in 3 </Td> <Td> Twice a week </Td> </Tr> <Tr> <Td> μ ± 1.5 σ </Td> <Td> 0.866 385 597 462 284 </Td> <Td> 1 in 7 </Td> <Td> Weekly </Td> </Tr> <Tr> <Td> μ ± 2σ </Td> <Td> 0.954 499 736 103 642 </Td> <Td> 1 in 22 </Td> <Td> Every three weeks </Td> </Tr> <Tr> <Td> μ ± 2.5 σ </Td> <Td> 0.987 580 669 348 448 </Td> <Td> 1 in 81 </Td> <Td> Quarterly </Td> </Tr> <Tr> <Td> μ ± 3σ </Td> <Td> 0.997 300 203 936 740 </Td> <Td> 1 in 370 </Td> <Td> Yearly </Td> </Tr> <Tr> <Td> μ ± 3.5 σ </Td> <Td> 0.999 534 741 841 929 </Td> <Td> 1 in 2149 </Td> <Td> Every six years </Td> </Tr> <Tr> <Td> μ ± 4σ </Td> <Td> 0.999 936 657 516 334 </Td> <Td> 1 in 7004157870000000000 ♠ 15 787 </Td> <Td> Every 43 years (twice in a lifetime) </Td> </Tr> <Tr> <Td> μ ± 4.5 σ </Td> <Td> 0.999 993 204 653 751 </Td> <Td> 1 in 7005147160000000000 ♠ 147 160 </Td> <Td> Every 403 years (once in the modern era) </Td> </Tr> <Tr> <Td> μ ± 5σ </Td> <Td> 0.999 999 426 696 856 </Td> <Td> 1 in 7006174427800000000 ♠ 1744278 </Td> <Td> Every 7003477600000000000 ♠ 4776 years (once in recorded history) </Td> </Tr> <Tr> <Td> μ ± 5.5 σ </Td> <Td> 0.999 999 962 020 875 </Td> <Td> 1 in 7007263302540000000 ♠ 26 330 254 </Td> <Td> Every 7004720900000000000 ♠ 72 090 years (thrice in history of modern humankind) </Td> </Tr> <Tr> <Td> μ ± 6σ </Td> <Td> 0.999 999 998 026 825 </Td> <Td> 1 in 7008506797346000000 ♠ 506 797 346 </Td> <Td> Every 1.38 million years (twice in history of humankind) </Td> </Tr> <Tr> <Td> μ ± 6.5 σ </Td> <Td> 0.999 999 999 919 680 </Td> <Td> 1 in 7010124501973930000 ♠ 12 450 197 393 </Td> <Td> Every 34 million years (halfway since the extinction of dinosaurs) </Td> </Tr> <Tr> <Td> μ ± 7σ </Td> <Td> 0.999 999 999 997 440 </Td> <Td> 1 in 7011390682215445000 ♠ 390 682 215 445 </Td> <Td> Every 1.07 billion years (a quarter of Earth's history) </Td> </Tr> <Tr> <Td> μ ± x σ </Td> <Td> erf ⁡ (x 2) (\ displaystyle \ operatorname (erf) \ left ((\ frac (x) (\ sqrt (2))) \ right)) </Td> <Td> 1 in 1 1 − erf ⁡ (x 2) (\ displaystyle (\ tfrac (1) (1 - \ operatorname (erf) \ left ((\ frac (x) (\ sqrt (2))) \ right)))) </Td> <Td> Every 1 1 − erf ⁡ (x 2) (\ displaystyle (\ tfrac (1) (1 - \ operatorname (erf) \ left ((\ frac (x) (\ sqrt (2))) \ right)))) days </Td> </Tr> </Table> <Tr> <Th> Range </Th> <Th> Expected fraction of population inside range </Th> <Th> Approximate expected frequency outside range </Th> <Th> Approximate frequency for daily event </Th> </Tr> <Tr> <Td> μ ± 0.5 σ </Td> <Td> 0.382 924 922 548 026 </Td> <Td> 2 in 3 </Td> <Td> Four times a week </Td> </Tr>

What percent of the population falls within 1 standard deviation of the mean