OFFSET
-9,1
COMMENTS
The probability P{(x-m)/s > 6} 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 six standard deviations is considered certain and "experimentally confirmed".
LINKS
Stanislav Sykora, Table of n, a(n) for n = -9..1991
Wikipedia, Normal distribution
FORMULA
P{(x-m)/s > 6} = P{(x-m)/s < -6} = 0.5*erfc(6/sqrt(2)) = erfc(3*sqrt(2))/2, with erfc(x) being the complementary error function.
EXAMPLE
9.86587645037698140700864132398042018669791249979028722477...e-10
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 6], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=6; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 18 2014
STATUS
approved