{"id":276,"date":"2023-08-03T05:14:26","date_gmt":"2023-08-03T05:14:26","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%82%b5%e3%83%b3%e3%83%95%e3%82%9a%e3%83%aa%e3%83%b3%e3%82%af%e3%82%99%e6%af%94%e7%8e%87%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T05:14:26","modified_gmt":"2023-08-03T05:14:26","slug":"%e3%82%b5%e3%83%b3%e3%83%95%e3%82%9a%e3%83%aa%e3%83%b3%e3%82%af%e3%82%99%e6%af%94%e7%8e%87%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%82%b5%e3%83%b3%e3%83%95%e3%82%9a%e3%83%aa%e3%83%b3%e3%82%af%e3%82%99%e6%af%94%e7%8e%87%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5272\u5408\u306e\u6a19\u672c\u5206\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u306b\u304a\u3051\u308b\u5272\u5408\u306e\u6a19\u672c\u5206\u5e03\u3068\u306f\u4f55\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u6bd4\u4f8b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5206\u5e03\u306e\u516c\u5f0f\u3068\u3001\u3055\u3089\u306b\u30b9\u30c6\u30c3\u30d7\u30d0\u30a4\u30b9\u30c6\u30c3\u30d7\u3067\u89e3\u6c7a\u3059\u308b\u7df4\u7fd2\u554f\u984c\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral-de-la-proporcion\"><\/span>\u5272\u5408\u306e\u6a19\u672c\u5206\u5e03\u306f\u3069\u3046\u306a\u308b\u3067\u3057\u3087\u3046\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5272\u5408\u306e\u6a19\u672c\u5206\u5e03<\/strong>(\u307e\u305f\u306f<strong>\u5272\u5408\u306e\u6a19\u672c\u5206\u5e03<\/strong>) \u306f\u3001\u6bcd\u96c6\u56e3\u304b\u3089\u8003\u3048\u3089\u308c\u308b\u5404\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3092\u8a08\u7b97\u3057\u3066\u5f97\u3089\u308c\u308b\u5206\u5e03\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6bcd\u96c6\u56e3\u304b\u3089\u5f97\u3089\u308c\u308b\u3059\u3079\u3066\u306e\u30b5\u30f3\u30d7\u30eb\u306e<a href=\"https:\/\/statorials.org\/ja\/\u30b5\u30f3\u30d5\u309a\u30eb\u306e\u5272\u5408\/\">\u6a19\u672c\u6bd4\u7387<\/a>\u304c\u3001\u305d\u306e\u6bd4\u7387\u306e\u6a19\u672c\u5206\u5e03\u3092\u5f62\u6210\u3057\u307e\u3059\u3002<\/p>\n<p>\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u6bd4\u7387\u306e\u6a19\u672c\u5206\u5e03\u306f\u3001\u6bcd\u96c6\u56e3\u304b\u3089\u9078\u629e\u3067\u304d\u308b\u3059\u3079\u3066\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u8abf\u67fb\u3057\u3001\u5404\u30b5\u30f3\u30d7\u30eb\u306e\u6a19\u672c\u6bd4\u7387\u3092\u5c0e\u51fa\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u8a08\u7b97\u3055\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306e\u30bb\u30c3\u30c8\u306f\u3001\u6bd4\u7387\u306e\u30b5\u30f3\u30d7\u30eb\u5206\u5e03\u3092\u69cb\u6210\u3057\u307e\u3059\u3002<\/p>\n<p>\u6bd4\u7387\u306e\u6a19\u672c\u5206\u5e03\u304c\u4f55\u306e\u305f\u3081\u306b\u3042\u308b\u306e\u304b\u7591\u554f\u306b\u601d\u3063\u3066\u3044\u308b\u5834\u5408\u306f\u3001\u7d71\u8a08\u3067\u306f\u3001\u5358\u4e00\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u5206\u6790\u3059\u308b\u3068\u304d\u306b\u6bcd\u96c6\u56e3\u306e\u6bd4\u7387\u306e\u5024\u306b\u8fd1\u3065\u304f\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u5e73\u5747\u5024\u306e\u6a19\u672c\u5206\u5e03\/\">\u5e73\u5747\u5024\u306e\u6a19\u672c\u5206\u5e03<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-proporcion\"><\/span>\u6bd4\u4f8b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5206\u5e03\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5b9f\u969b\u3001\u30b5\u30f3\u30d7\u30eb\u306e\u4e00\u90e8\u3092\u8abf\u67fb\u3059\u308b\u3068\u304d\u306f\u3001\u6210\u529f\u4e8b\u4f8b\u3092\u5206\u6790\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7814\u7a76\u306e\u78ba\u7387\u5909\u6570\u306f<a href=\"https:\/\/statorials.org\/ja\/\u4e8c\u9805\u5206\u5e03-1\/\">\u4e8c\u9805\u78ba\u7387\u5206\u5e03<\/a>\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u306b\u3088\u308c\u3070\u3001\u5927\u304d\u306a\u30b5\u30a4\u30ba (n&gt;30) \u306e\u5834\u5408\u3001\u4e8c\u9805\u5206\u5e03\u3092\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u6bd4\u7387\u306e\u6a19\u672c\u5206\u5e03\u306f\u3001\u6b21\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u4f7f\u7528\u3057\u3066\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f3408076893f390bb65baecfe38e6eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{p}=p \\qquad \\sigma_{p}=\\sqrt{\\frac{pq}{n}}\\\\[4ex]\\displaystyle N_{p}\\left(p, \\sqrt{\\frac{pq}{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"168\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u91d1<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u6210\u529f\u306e\u78ba\u7387\u3067\u3042\u308a\u3001<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5931\u6557\u306e\u78ba\u7387\u3067\u3059<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3002<\/p>\n<p><strong>\u6ce8:<\/strong>\u4e8c\u9805\u5206\u5e03\u306f\u3001\u6b21\u306e\u5834\u5408\u306b\u306e\u307f\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u4f3c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-88e275a965c091eb810599a07b0f8d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>30&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;52&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<p> \u3001<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-41130f51ca4b83f1bf25b9dde90ecbfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"np\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u305d\u3057\u3066<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0af2ac5b6eb874f65b406b3bc39f0c7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"nq\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3002 <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u6b63\u898f\u5206\u5e03\/\">\u6b63\u898f\u5206\u5e03\u306e\u4f8b<\/a><\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5272\u5408\u306e\u6a19\u672c\u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u4f3c\u3067\u304d\u308b\u305f\u3081\u3001<strong>\u6a19\u672c\u306e\u5272\u5408\u306b\u95a2\u9023\u3059\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f\u6b21<\/strong>\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5b7a4224240587268d0dd7865a33ac31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"78\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3067\u3059\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u4eba\u53e3\u306b\u5360\u3081\u308b\u5272\u5408\u3067\u3059\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u6bcd\u96c6\u56e3\u304c\u5931\u6557\u3059\u308b\u78ba\u7387\u3067\u3042\u308a\u3001<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u306f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u3059\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u306f\u3001\u6a19\u6e96\u6b63\u898f\u5206\u5e03 N(0,1) \u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5909\u6570\u3067\u3059\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-distribucion-muestral-de-la-proporcion\"><\/span>\u6bd4\u4f8b\u62bd\u51fa\u5206\u5e03\u306e\u5177\u4f53\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6bd4\u4f8b\u6a19\u672c\u5206\u5e03\u306e\u5b9a\u7fa9\u3068\u305d\u308c\u306b\u95a2\u9023\u3059\u308b\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u6982\u5ff5\u3092\u5b8c\u5168\u306b\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3057\u305f\u4f8b\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u3042\u308b\u7523\u696d\u4f1a\u793e\u306f\u3001\u6b20\u9665\u90e8\u54c1\u304c 3% \u3057\u304b\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u90e8\u54c1\u3092\u88fd\u9020\u3057\u3066\u3044\u308b\u3068\u4e3b\u5f35\u3059\u308b\u5de5\u5834\u304b\u3089\u90e8\u54c1\u306e\u30d0\u30c3\u30c1\u3092\u8cfc\u5165\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u78ba\u8a8d\u3059\u308b\u305f\u3081\u306b\u3001\u540c\u793e\u306f 500 \u500b\u306e\u90e8\u54c1\u306e\u6ce8\u6587\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3057\u305f\u3002\u30b5\u30f3\u30d7\u30eb\u5185\u3067 5% \u3092\u8d85\u3048\u308b\u6b20\u9665\u90e8\u54c1\u304c\u898b\u3064\u304b\u308b\u78ba\u7387\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?<\/li>\n<\/ul>\n<p>\u3053\u306e\u5834\u5408\u3001\u8abf\u67fb\u3057\u305f\u3044\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u306f 0.03 \u3067\u3042\u308b\u305f\u3081\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc q \u306f 0.97 \u306b\u76f8\u5f53\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4354c268853ec7b592bcacd23f3b214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}p=0,03\\\\[2ex]q=1-p=0,97\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"130\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5f7c\u3089\u304c\u5c0b\u306d\u308b\u78ba\u7387\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u898b\u305f\u5f0f\u3092\u9069\u7528\u3057\u3066\u3001\u5bfe\u5fdc\u3059\u308b\u7d71\u8a08\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-647d67d275bb8a7fbeb60f7ae464c0fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" 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href=\"https:\/\/statorials.org\/ja\/\u6b63\u898f\u5206\u5e03\u8868\/\">Z \u5206\u5e03\u8868<\/a>\u3067 P[Z\u22642.62] \u306e\u78ba\u7387\u3092\u63a2\u3057\u3001\u554f\u984c\u304c\u6c42\u3081\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-812f9b97c53e15da88b0cb7149f254c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P\\left[\\widehat{p}>0,05\\right]=\\\\[2ex]=P[Z>2,62]=\\\\[2ex]=1-P[Z\\leq 2,62]=\\\\[2ex]=1-0,9956=\\\\[2ex]=0,0044\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;167&#8243; width=&#8221;162&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<p>\u7d50\u8ad6\u3068\u3057\u3066\u3001\u5206\u6790\u3055\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u3067 5% 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