

A239384


Decimal expansion of the probability of a normalerror variable exceeding the mean by more than three standard deviations.


7



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
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OFFSET

2,2


COMMENTS

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


EXAMPLE

0.0013498980316300945266518147675949773778293681583806493642...


PROG

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


CROSSREFS

Cf. P{(xm)/s>n}: A239382 (n=1), A239383 (n=2), A239385 (n=4), A239386 (n=5), A239387 (n=6).
Sequence in context: A285265 A178590 A022463 * A242219 A106833 A217578
Adjacent sequences: A239381 A239382 A239383 * A239385 A239386 A239387


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Mar 18 2014


STATUS

approved



