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A239384
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Decimal expansion of the probability of a normal-error variable exceeding the mean by more than three standard deviations.
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7
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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
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OFFSET
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-2,2
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COMMENTS
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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.
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LINKS
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FORMULA
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P{(x-m)/s > 3} = P{(x-m)/s < -3} = 0.5*erfc(3/sqrt(2)), with erfc(x) being the complementary error function.
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EXAMPLE
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0.0013498980316300945266518147675949773778293681583806493642...
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MATHEMATICA
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First[RealDigits[1 - CDF[NormalDistribution[], 3], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)
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PROG
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(PARI) n=3; a=0.5*erfc(n/sqrt(2)) \\ Use sufficient realprecision
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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