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A178647 Decimal expansion of the fraction of a population falling within +- 1 standard deviation of the mean, assuming a normal distribution.

%I A178647 #32 Feb 16 2025 08:33:12
%S A178647 6,8,2,6,8,9,4,9,2,1,3,7,0,8,5,8,9,7,1,7,0,4,6,5,0,9,1,2,6,4,0,7,5,8,
%T A178647 4,4,9,5,5,8,2,5,9,3,3,4,5,3,2,0,8,7,8,1,9,7,4,7,8,8,9,0,0,4,8,5,9,8,
%U A178647 2,8,8,3,9,7,4,4,0,9,6,5,9,0,0,1,7,6,9,8,3,6,8,1,1,2,7,8,6,5,5,0,5,6,5,4,5
%N A178647 Decimal expansion of the fraction of a population falling within +- 1 standard deviation of the mean, assuming a normal distribution.
%D A178647 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 40, table 40:7:1 at page 387.
%H A178647 Rick L. Shepherd, <a href="/A178647/b178647.txt">Table of n, a(n) for n = 0..10000</a>
%H A178647 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Erf.html">Erf</a>.
%H A178647 Wikipedia, <a href="http://en.wikipedia.org/wiki/68-95-99.7_rule">68-95-99.7 rule</a>.
%F A178647 Equals erf(1/sqrt(2)). - _Jean-François Alcover_, May 29 2013
%e A178647 0.6826894921370858971704650912640758449558259334532087819747889004859...
%p A178647 erf(1/sqrt(2)) ; evalf(%) ; # _R. J. Mathar_, Mar 22 2016
%t A178647 RealDigits[(1 + Erf[1/Sqrt@2])/2 - (1 + Erf[ -1/Sqrt@2])/2, 10, 111][[1]] (* _Robert G. Wilson v_, Jun 01 2010 *)
%o A178647 (MATLAB) 0.5*(1+erf(1/sqrt(2)))- 0.5*(1+erf(-1/sqrt(2)))
%o A178647 (PARI) (erfc(-1/sqrt(2))-erfc(1/sqrt(2)))/2 \\ _Charles R Greathouse IV_, Sep 04 2012
%o A178647 (PARI) 1 - erfc(1/sqrt(2)) \\ _Rick L. Shepherd_, Mar 05 2014
%Y A178647 Cf. A110894 (2sigma), A270712 (3sigma).
%K A178647 nonn,cons
%O A178647 0,1
%A A178647 _Joost de Winter_, May 31 2010
%E A178647 More terms from _Robert G. Wilson v_, Jun 01 2010
%E A178647 Edited by _N. J. A. Sloane_, Jun 07 2010