A239387 - OEIS

%I #11 Jun 14 2022 01:43:06

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

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

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

%C The probability P{(x-m)/s > 6} 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 six standard deviations is considered certain and "experimentally confirmed".

%H Stanislav Sykora, <a href="/A239387/b239387.txt">Table of n, a(n) for n = -9..1991</a>

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

%F 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.

%e 9.86587645037698140700864132398042018669791249979028722477...e-10

%t First[RealDigits[1 - CDF[NormalDistribution[], 6], 10, 100]] (* _Joan Ludevid_, Jun 13 2022 *)

%o (PARI) n=6;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), A239386 (n=5).

%K nonn,cons

%O -9,1

%A _Stanislav Sykora_, Mar 18 2014