<P> For various values of z, the percentage of values expected to lie in and outside the symmetric interval, CI = (− zσ, zσ), are as follows: </P> <Table> <Tr> <Th> Confidence interval </Th> <Th> Proportion within </Th> <Th_colspan="2"> Proportion without </Th> </Tr> <Tr> <Th> Percentage </Th> <Th> Percentage </Th> <Th> Fraction </Th> </Tr> <Tr> <Td> 6999674490000000000 ♠ 0.674 490 σ </Td> <Td> 7001500000000000000 ♠ 50% </Td> <Td> 7001500000000000000 ♠ 50% </Td> <Td> 1 / 7000200000000000000 ♠ 2 </Td> </Tr> <Tr> <Td> 6999994458000000000 ♠ 0.994 458 σ </Td> <Td> 68% </Td> <Td> 32% </Td> <Td> 1 / 3.125 </Td> </Tr> <Tr> <Td> 1σ </Td> <Td> 7001682689492000000 ♠ 68.268 9492% </Td> <Td> 7001317310508000000 ♠ 31.731 0508% </Td> <Td> 1 / 7000315148720000000 ♠ 3.151 4872 </Td> </Tr> <Tr> <Td> 7000128155200000000 ♠ 1.281 552 σ </Td> <Td> 80% </Td> <Td> 20% </Td> <Td> 1 / 5 </Td> </Tr> <Tr> <Td> 7000164485400000000 ♠ 1.644 854 σ </Td> <Td> 90% </Td> <Td> 10% </Td> <Td> 1 / 10 </Td> </Tr> <Tr> <Td> 7000195996400000000 ♠ 1.959 964 σ </Td> <Td> 95% </Td> <Td> 5% </Td> <Td> 1 / 20 </Td> </Tr> <Tr> <Td> 2σ </Td> <Td> 7001954499736000000 ♠ 95.449 9736% </Td> <Td> 7000455002640000000 ♠ 4.550 0264% </Td> <Td> 1 / 7001219778950000000 ♠ 21.977 895 </Td> </Tr> <Tr> <Td> 7000257582900000000 ♠ 2.575 829 σ </Td> <Td> 99% </Td> <Td> 1% </Td> <Td> 1 / 100 </Td> </Tr> <Tr> <Td> 3σ </Td> <Td> 7001997300204000000 ♠ 99.730 0204% </Td> <Td> 6999269979600000000 ♠ 0.269 9796% </Td> <Td> 1 / 370.398 </Td> </Tr> <Tr> <Td> 7000329052700000000 ♠ 3.290 527 σ </Td> <Td> 99.9% </Td> <Td> 0.1% </Td> <Td> 1 / 7003100000000000000 ♠ 1000 </Td> </Tr> <Tr> <Td> 7000389059200000000 ♠ 3.890 592 σ </Td> <Td> 99.99% </Td> <Td> 0.01% </Td> <Td> 1 / 7004100000000000000 ♠ 10 000 </Td> </Tr> <Tr> <Td> 4σ </Td> <Td> 7001999936660000000 ♠ 99.993 666% </Td> <Td> 6997633400000000000 ♠ 0.006 334% </Td> <Td> 1 / 7004157870000000000 ♠ 15 787 </Td> </Tr> <Tr> <Td> 7000441717300000000 ♠ 4.417 173 σ </Td> <Td> 99.999% </Td> <Td> 0.001% </Td> <Td> 1 / 7005100000000000000 ♠ 100 000 </Td> </Tr> <Tr> <Td> 7000450000000000000 ♠ 4.5 σ </Td> <Td> 99.999 320 465 3751% </Td> <Td> 0.000 679 534 6249% </Td> <Td> 3.4 / 7006100000000000000 ♠ 1000000 (on each side of mean) </Td> </Tr> <Tr> <Td> 7000489163800000000 ♠ 4.891 638 σ </Td> <Td> 7001999999000000000 ♠ 99.9999% </Td> <Td> 6996100000000000000 ♠ 0.0001% </Td> <Td> 1 / 7006100000000000000 ♠ 1000000 </Td> </Tr> <Tr> <Td> 5σ </Td> <Td> 7001999999426697000 ♠ 99.999 942 6697% </Td> <Td> 6995573303000000000 ♠ 0.000 057 3303% </Td> <Td> 1 / 7006174427800000000 ♠ 1744278 </Td> </Tr> <Tr> <Td> 7000532672399999999 ♠ 5.326 724 σ </Td> <Td> 7001999999900000000 ♠ 99.999 99% </Td> <Td> 6995100000000000000 ♠ 0.000 01% </Td> <Td> 1 / 7007100000000000000 ♠ 10 000 000 </Td> </Tr> <Tr> <Td> 7000573072900000000 ♠ 5.730 729 σ </Td> <Td> 7001999999990000000 ♠ 99.999 999% </Td> <Td> 6994100000000000000 ♠ 0.000 001% </Td> <Td> 1 / 7008100000000000000 ♠ 100 000 000 </Td> </Tr> <Tr> <Td> 6σ </Td> <Td> 7001999999998027000 ♠ 99.999 999 8027% </Td> <Td> 6993197300000000000 ♠ 0.000 000 1973% </Td> <Td> 1 / 7008506797346000000 ♠ 506 797 346 </Td> </Tr> <Tr> <Td> 7000610941000000000 ♠ 6.109 410 σ </Td> <Td> 7001999999999000000 ♠ 99.999 9999% </Td> <Td> 6993100000000000000 ♠ 0.000 0001% </Td> <Td> 1 / 7009100000000000000 ♠ 1000000000 </Td> </Tr> <Tr> <Td> 7000646695100000000 ♠ 6.466 951 σ </Td> <Td> 7001999999999900000 ♠ 99.999 999 99% </Td> <Td> 6992100000000000000 ♠ 0.000 000 01% </Td> <Td> 1 / 7010100000000000000 ♠ 10 000 000 000 </Td> </Tr> <Tr> <Td> 7000680650200000000 ♠ 6.806 502 σ </Td> <Td> 7001999999999990000 ♠ 99.999 999 999% </Td> <Td> 6991100000000000000 ♠ 0.000 000 001% </Td> <Td> 1 / 7011100000000000000 ♠ 100 000 000 000 </Td> </Tr> <Tr> <Td> 7σ </Td> <Td> 99.999 999 999 7440% </Td> <Td> 6990256000000000000 ♠ 0.000 000 000 256% </Td> <Td> 1 / 7011390682215445000 ♠ 390 682 215 445 </Td> </Tr> </Table> <Tr> <Th> Confidence interval </Th> <Th> Proportion within </Th> <Th_colspan="2"> Proportion without </Th> </Tr> <Tr> <Th> Percentage </Th> <Th> Percentage </Th> <Th> Fraction </Th> </Tr>

When is the mean equal to the standard deviation