There is occasionally a need to know probabilities or confidences
associated with large sigmas. There have been posts here in the past
asking for such information. I posted one of them myself. I finally
decided to do something about it.
N, P: the probability of a sample lying outside the interval [m-
N*sigma,+N*sigma]
1, 0.3173105078629141028295349087359241550441740665467912180252...
2, 0.0455002638963584144005652743330668749435524474033568679673...
3, 0.0026997960632601890533036295351899547556587363167612987284...
4, 0.0000633424836662398425075415134443025968876667509605530170...
5, 5.7330314375838782334750466574929070770884602722377914... x 10^-7
6, 1.9731752900753962814017282647960840373395824999580574... x 10^-9
7, 2.559625087771670008767247381561665996065688308397435... x 10^-12
8, 1.244192114854356824703199034517637684497743455780055... x 10^-15
9, 2.257176811907681295471004151937494515960083801636329... x 10^-19
10, 1.523970604832105213194668650319861672700806655591392... x 10^-23
11, 3.821319148997351422300831267415581399535743423428077... x 10^-28
12, 3.552964224155357995392342003691114184785332868357906... x 10^-33
13, 1.223432879909975936455041954508814229022578305657873... x 10^-38
14, 1.558707363838560050871936367779017227111583302922144... x 10^-44
15, 7.341932398625501771572179310669486972832503256080314... x 10^-51
I calculated the above using erfc(N/(2^(1/2)) in Wolfram's wonderful
calculator at:
http://www.wolframalpha.com/
Mathematica is infinitely cool.
Note, 1 - P = 1 - erfc(N/(2^(1/2)) is probability of a value being
within [m-N*sigma,+N*sigma]. For more information on standard
deviation see:
http://en.wikipedia.org/wiki/Standard_deviation
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
