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A239385
Decimal expansion of the probability of a normal-error 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
OFFSET
-4,1
COMMENTS
The probability P{(x-m)/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
FORMULA
P{(x-m)/s > 4} = P{(x-m)/s < -4} = 0.5*erfc(4/sqrt(2)) = erfc(2*sqrt(2))/2, with erfc(x) being the complementary error function.
EXAMPLE
0.000031671241833119921253770756722151298443833375480276508549331722...
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 4], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=4; 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), A239386 (n=5), A239387 (n=6).
Sequence in context: A112692 A291217 A198614 * A124929 A208766 A259454
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 18 2014
STATUS
approved