正規分布を仮定した偏差値と上位%の関係

50桁の精度で数値計算した値です。以下JSON形式で、σ、偏差値、上位何%にあたるかの順に偏差値0.1刻みで平均値0σ(偏差値50)から7σ(偏差値120)まで載せてあります。

[
 [
 "0.",
 "50.",
 "50.000000000000000000000000000000000000000000000000 %"
 ],
 [
 "0.01",
 "50.1",
 "49.601064368536839629821000209153643587961780092740 %"
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 [
 "0.02",
 "50.2",
 "49.202168628309801897367224029406908452261375119747 %"
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 [
 "0.03",
 "50.3",
 "48.803352658588735536112089593476373511187063357981 %"
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 [
 "0.04",
 "50.4",
 "48.404656314716923860157369110617763396216286717350 %"
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 [
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 [
 "0.06",
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 [
 "0.07",
 "50.7",
 "47.209682981947889641156318377818150528270383437112 %"
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 [
 "0.08",
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 [
 "0.09",
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 ],
 [
 "0.1",
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 "46.017216272297101853459538176081791698593771631023 %"
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 [
 "0.11",
 "51.1",
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 [
 "0.12",
 "51.2",
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 [
 "0.13",
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 [
 "0.14",
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 "44.432999519409357091569320341592623401820585420668 %"
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 [
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 [
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 [
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 [
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