A239384 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than three standard deviations.

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

Offset

-2,2

Comments

The probability P{(x-m)/s > 3} 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 three standard deviations is considered fairly significant, unless it is an isolated case among hundreds of measurements.

Links

Stanislav Sykora, Table of n, a(n) for n = -2..1998

Wikipedia, Normal distribution

Formula

P{(x-m)/s > 3} = P{(x-m)/s < -3} = 0.5*erfc(3/sqrt(2)), with erfc(x) being the complementary error function.

Example

0.0013498980316300945266518147675949773778293681583806493642...

Mathematica

First[RealDigits[1 - CDF[NormalDistribution[], 3], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)

Prog

(PARI) n=3; a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision

Crossrefs

Cf. P{(x-m)/s>n}: A239382 (n=1), A239383 (n=2), A239385 (n=4), A239386 (n=5), A239387 (n=6).

Sequence in context: A178590 A022463 A378116 * A242219 A106833 A217578

Adjacent sequences: A239381 A239382 A239383 * A239385 A239386 A239387

Keyword

nonn,cons

Author

Stanislav Sykora, Mar 18 2014

Status

approved