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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 Stanislav Sykora, Table of n, a(n) for n = -6..1994 Wikipedia, Normal distribution 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 Adjacent sequences: A239383 A239384 A239385 * A239387 A239388 A239389 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.)