A239382 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than one standard deviation.

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

Offset

0,2

Comments

The probability P{(x-m)/s > 1} 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 just one standard deviation is not significant, unless corroborated by strong additional indications.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Wikipedia, Normal distribution

Formula

P{(x-m)/s > 1} = P{(x-m)/s < -1} = 0.5*erfc(1/sqrt(2)) = erfc(sqrt(2)/2)/2, with erfc(x) being the complementary error function.

Example

0.15865525393145705141476745436796207752208703327339560901260...

Mathematica

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

Prog

(PARI) n=1; a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision

Crossrefs

Cf. P{(x-m)/s>n}: A239383 (n=2), A239384 (n=3), A239385 (n=4), A239386 (n=5), A239387 (n=6).

Sequence in context: A102519 A334849 A199265 * A085117 A301862 A245944

Adjacent sequences: A239379 A239380 A239381 * A239383 A239384 A239385

Keyword

nonn,cons

Author

Stanislav Sykora, Mar 17 2014

Status

approved