OFFSET
-4,1
COMMENTS
The probability P{(x-m)/s > 4} 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 four standard deviations is considered significant, unless it is an isolated case among thousands of iterated measurements.
LINKS
Stanislav Sykora, Table of n, a(n) for n = -4..1996
Wikipedia, Normal distribution
FORMULA
P{(x-m)/s > 4} = P{(x-m)/s < -4} = 0.5*erfc(4/sqrt(2)) = erfc(2*sqrt(2))/2, with erfc(x) being the complementary error function.
EXAMPLE
0.000031671241833119921253770756722151298443833375480276508549331722...
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 4], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=4; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 18 2014
STATUS
approved