

A239386


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


7



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

6,1


COMMENTS

The probability P{(xm)/s > 5} 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 five standard deviations is considered practically certain, unless it is an isolated case among tens of thousands of iterated measurements.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 6..1994
Wikipedia, Normal distribution


FORMULA

P{(xm)/s > 5} = P{(xm)/s < 5} = 0.5*erfc(5/sqrt(2)), with erfc(x) being the complementary error function.


EXAMPLE

2.86651571879193911673752332874645353854423013611889573...e7


PROG

(PARI) n=5; 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), A239387 (n=6).
Sequence in context: A021353 A131361 A228042 * A011370 A021890 A199504
Adjacent sequences: A239383 A239384 A239385 * A239387 A239388 A239389


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Mar 18 2014


STATUS

approved



