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

Author

Stanislav Sykora, Mar 17 2014

Keywords

• nonn
• cons

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.

Examples

			0.15865525393145705141476745436796207752208703327339560901260...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Wikipedia, Normal distribution

Crossrefs

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

Programs

Mathematica

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

PARI

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

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.