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A239386 Decimal expansion of the probability of a normal-error 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
-6,1
COMMENTS
The probability P{(x-m)/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
FORMULA
P{(x-m)/s > 5} = P{(x-m)/s < -5} = 0.5*erfc(5/sqrt(2)), with erfc(x) being the complementary error function.
EXAMPLE
2.86651571879193911673752332874645353854423013611889573...e-7
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 5], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=5; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
CROSSREFS
Cf. P{(x-m)/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
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 18 2014
STATUS
approved

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Last modified April 17 12:39 EDT 2024. Contains 371763 sequences. (Running on oeis4.)