

A239387


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


7



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

9,1


COMMENTS

The probability P{(xm)/s > 6} 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 six standard deviations is considered certain and "experimentally confirmed".


LINKS

Stanislav Sykora, Table of n, a(n) for n = 9..1991
Wikipedia, Normal distribution


FORMULA

P{(xm)/s > 6} = P{(xm)/s < 6} = 0.5*erfc(6/sqrt(2)) = erfc(3*sqrt(2))/2, with erfc(x) being the complementary error function.


EXAMPLE

9.86587645037698140700864132398042018669791249979028722477...e10


PROG

(PARI) n=6; 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), A239385 (n=4), A239386 (n=5).
Sequence in context: A248585 A105415 A197015 * A226735 A155920 A082124
Adjacent sequences: A239384 A239385 A239386 * A239388 A239389 A239390


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Mar 18 2014


STATUS

approved



