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Decimal expansion of the probability of a normal-error variable exceeding the mean by more than five standard deviations.
7

%I #10 Jun 14 2022 01:43:01

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

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

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

%C The probability P{(x-m)/s > 5} 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 five standard deviations is considered practically certain, unless it is an isolated case among tens of thousands of iterated measurements.

%H Stanislav Sykora, <a href="/A239386/b239386.txt">Table of n, a(n) for n = -6..1994</a>

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

%F P{(x-m)/s > 5} = P{(x-m)/s < -5} = 0.5*erfc(5/sqrt(2)), with erfc(x) being the complementary error function.

%e 2.86651571879193911673752332874645353854423013611889573...e-7

%t First[RealDigits[1 - CDF[NormalDistribution[], 5], 10, 100]] (* _Joan Ludevid_, Jun 13 2022 *)

%o (PARI) n=5;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), A239385 (n=4), A239387 (n=6).

%K nonn,cons

%O -6,1

%A _Stanislav Sykora_, Mar 18 2014