OFFSET
0,2
COMMENTS
The probability P{(x-m)/s > 1} 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 just one standard deviation is not significant, unless corroborated by strong additional indications.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
Wikipedia, Normal distribution
FORMULA
P{(x-m)/s > 1} = P{(x-m)/s < -1} = 0.5*erfc(1/sqrt(2)) = erfc(sqrt(2)/2)/2, with erfc(x) being the complementary error function.
EXAMPLE
0.15865525393145705141476745436796207752208703327339560901260...
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 1], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=1; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 17 2014
STATUS
approved