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A239382 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than one standard deviation. 7
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Wikipedia, Normal distribution

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.

EXAMPLE

0.15865525393145705141476745436796207752208703327339560901260...

PROG

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

CROSSREFS

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

Sequence in context: A136258 A102519 A199265 * A085117 A245944 A160043

Adjacent sequences:  A239379 A239380 A239381 * A239383 A239384 A239385

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Mar 17 2014

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.