A239385 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than four standard deviations.

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, 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

Offset

-4,1

Comments

The probability P{(x-m)/s > 4} 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 four standard deviations is considered significant, unless it is an isolated case among thousands of iterated measurements.

Links

Stanislav Sykora, Table of n, a(n) for n = -4..1996

Wikipedia, Normal distribution

Formula

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.

Example

0.000031671241833119921253770756722151298443833375480276508549331722...

Mathematica

First[RealDigits[1 - CDF[NormalDistribution[], 4], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)

Prog

(PARI) n=4; 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), A239386 (n=5), A239387 (n=6).

Sequence in context: A112692 A291217 A198614 * A124929 A208766 A259454

Adjacent sequences: A239382 A239383 A239384 * A239386 A239387 A239388

Keyword

nonn,cons

Author

Stanislav Sykora, Mar 18 2014

Status

approved