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A239384
Decimal expansion of the probability of a normal-error variable exceeding the mean by more than three standard deviations.
7
1, 3, 4, 9, 8, 9, 8, 0, 3, 1, 6, 3, 0, 0, 9, 4, 5, 2, 6, 6, 5, 1, 8, 1, 4, 7, 6, 7, 5, 9, 4, 9, 7, 7, 3, 7, 7, 8, 2, 9, 3, 6, 8, 1, 5, 8, 3, 8, 0, 6, 4, 9, 3, 6, 4, 2, 2, 1, 9, 8, 5, 3, 5, 5, 8, 0, 5, 7, 2, 0
OFFSET
-2,2
COMMENTS
The probability P{(x-m)/s > 3} 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 three standard deviations is considered fairly significant, unless it is an isolated case among hundreds of measurements.
LINKS
FORMULA
P{(x-m)/s > 3} = P{(x-m)/s < -3} = 0.5*erfc(3/sqrt(2)), with erfc(x) being the complementary error function.
EXAMPLE
0.0013498980316300945266518147675949773778293681583806493642...
MATHEMATICA
First[RealDigits[1 - CDF[NormalDistribution[], 3], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
PROG
(PARI) n=3; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
CROSSREFS
Cf. P{(x-m)/s>n}: A239382 (n=1), A239383 (n=2), A239385 (n=4), A239386 (n=5), A239387 (n=6).
Sequence in context: A330385 A178590 A022463 * A242219 A106833 A217578
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Mar 18 2014
STATUS
approved