

A239385


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


7



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
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OFFSET

4,1


COMMENTS

The probability P{(xm)/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{(xm)/s > 4} = P{(xm)/s < 4} = 0.5*erfc(4/sqrt(2)) = erfc(2*sqrt(2))/2, with erfc(x) being the complementary error function.


EXAMPLE

0.000031671241833119921253770756722151298443833375480276508549331722...


PROG

(PARI) n=4; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision


CROSSREFS

Cf. P{(xm)/s>n}: A239382 (n=1), A239383 (n=2), A239384 (n=3), A239386 (n=5), A239387 (n=6).
Sequence in context: A242729 A112692 A198614 * A124929 A208766 A259454
Adjacent sequences: A239382 A239383 A239384 * A239386 A239387 A239388


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Mar 18 2014


STATUS

approved



