A239387 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than six standard deviations.

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, 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

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

Cf. P{(x-m)/s>n}: A239382 (n=1), A239383 (n=2), A239384 (n=3), A239385 (n=4), A239386 (n=5).

Sequence in context: A105415 A346728 A197015 * A226735 A155920 A082124

Adjacent sequences: A239384 A239385 A239386 * A239388 A239389 A239390

Keyword

nonn,cons

Author

Stanislav Sykora, Mar 18 2014

Status

approved