A239385 - OEIS

%I #12 Jun 28 2026 15:48:08

%S 3,1,6,7,1,2,4,1,8,3,3,1,1,9,9,2,1,2,5,3,7,7,0,7,5,6,7,2,2,1,5,1,2,9,

%T 8,4,4,3,8,3,3,3,7,5,4,8,0,2,7,6,5,0,8,5,4,9,3,3,1,7,2,2,0,7,8,5,8,5,1

%N Decimal expansion of the probability of a normal-error variable exceeding the mean by more than four standard deviations.

%C The probability P{(x-m)/s > 4} for a normally distributed random variable x with mean m and standard deviation s.

%C 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.

%H Stanislav Sykora, <a href="/A239385/b239385.txt">Table of n, a(n) for n = -4..1996</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>

%F 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.

%e 0.000031671241833119921253770756722151298443833375480276508549331722...

%t First[RealDigits[1 - CDF[NormalDistribution[], 4], 10, 100]] (* _Joan Ludevid_, Jun 13 2022 *)

%o (PARI) n=4;a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision

%Y Cf. P{(x-m)/s>n}: A239382 (n=1), A239383 (n=2), A239384 (n=3), A239386 (n=5), A239387 (n=6).

%K nonn,cons,changed

%O -4,1

%A _Stanislav Sykora_, Mar 18 2014