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 A329280 Decimal expansion of the quantile z_0.9 of the standard normal distribution. 8
 1, 2, 8, 1, 5, 5, 1, 5, 6, 5, 5, 4, 4, 6, 0, 0, 4, 6, 6, 9, 6, 5, 1, 0, 3, 3, 2, 9, 4, 4, 8, 7, 4, 2, 8, 1, 8, 6, 1, 9, 9, 0, 7, 8, 2, 4, 3, 5, 2, 5, 8, 2, 6, 5, 9, 7, 0, 2, 6, 4, 8, 2, 3, 0, 5, 6, 5, 7, 0, 3, 3, 2, 4, 8, 1, 2, 2, 4, 5, 4, 3, 0, 1, 5, 5, 4, 3, 8, 1, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS z_p is the number z such that Phi(z) = p, where Phi(x) = Integral_{t=-oo..x} (1/sqrt(2*Pi))*exp(-t^2/2)*dt is the cumulative distribution function of the standard normal distribution. This sequence gives z_0.9 (also called the 9th decile or the 90th percentile). This number can also be denoted as probit(0.9), where probit(p) is the inverse function of Phi(x). See the Wikipedia link below. LINKS Eric Weisstein's World of Mathematics, Quantile Function Wikipedia, Probit FORMULA If X ~ N(0,1), then P(X<=1.2815515655...) = 0.9, P(X<=-1.2815515655...) = 0.1. PROG (PARI) default(realprecision, 100); solve(x=0, 5, erfc(x)-2*0.1)*sqrt(2) CROSSREFS Quantiles of the standard normal distribution: A092678 (z_0.75), this sequence (z_0.9), A329281 (z_0.95), A329282 (z_0.99), A329283 (z_0.995), A329284 (z_0.999), A329285 (z_0.9995), A329286 (z_0.9999), A329287 (z_0.99999), A329363 (z_0.999999). Sequence in context: A275980 A156029 A120026 * A109089 A200479 A198873 Adjacent sequences:  A329277 A329278 A329279 * A329281 A329282 A329283 KEYWORD nonn,cons AUTHOR Jianing Song, Nov 12 2019 STATUS approved

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Last modified February 25 11:17 EST 2020. Contains 332234 sequences. (Running on oeis4.)