OFFSET
-1,1
COMMENTS
The probability P{(x-m)/s > 2} for a normally distributed random variable x with mean m and standard deviation s. In experimental sciences (hypothesis testing), a measured excursion exceeding background "noise" by more than two standard deviations is considered mildly significant if corroborated by additional indications.
LINKS
Stanislav Sykora, Table of n, a(n) for n = -1..1999
Wikipedia, Normal distribution
FORMULA
P{(x-m)/s > 2} = P{(x-m)/s < -2} = 0.5*erfc(2/sqrt(2)) = erfc(sqrt(2))/2, with erfc(x) being the complementary error function.
EXAMPLE
0.0227501319481792072002826371665334374717762237016784339836660...
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 2], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=2; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 17 2014
STATUS
approved