{"id":278,"date":"2023-08-03T05:34:09","date_gmt":"2023-08-03T05:34:09","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%9d%87%e5%80%bc%e7%9a%84%e6%8a%bd%e6%a0%b7%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T05:34:09","modified_gmt":"2023-08-03T05:34:09","slug":"%e5%9d%87%e5%80%bc%e7%9a%84%e6%8a%bd%e6%a0%b7%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%9d%87%e5%80%bc%e7%9a%84%e6%8a%bd%e6%a0%b7%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u662f\u4ec0\u4e48\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u5e73\u5747\u62bd\u6837\u5206\u5e03\u516c\u5f0f\u548c\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral-de-la-media\"><\/span>\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03<\/strong>\uff08\u6216<strong>\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03<\/strong>\uff09\u662f\u901a\u8fc7\u8ba1\u7b97\u603b\u4f53\u4e2d\u6bcf\u4e2a\u53ef\u80fd\u6837\u672c\u7684\u62bd\u6837\u5747\u503c\u800c\u5f97\u5230\u7684\u5206\u5e03\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6765\u81ea\u603b\u4f53\u7684\u6240\u6709\u53ef\u80fd\u6837\u672c\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6837\u672c\u5e73\u5747\u503c\/\">\u6837\u672c<\/a>\u5747\u503c\u96c6\u5408\u5f62\u6210\u4e86\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u3002<\/p>\n<p>\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u7814\u7a76\u53ef\u4ee5\u4ece\u603b\u4f53\u4e2d\u62bd\u53d6\u7684\u6240\u6709\u6837\u672c\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u7684\u5e73\u5747\u503c\uff0c\u90a3\u4e48\u8ba1\u7b97\u503c\u7684\u96c6\u5408\u5c31\u5f62\u6210\u4e86\u6837\u672c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u7528\u4e8e\u8ba1\u7b97\u5206\u6790\u5355\u4e2a\u6837\u672c\u65f6\u63a5\u8fd1\u603b\u4f53\u5747\u503c\u7684\u6982\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-media\"><\/span>\u5747\u503c\u62bd\u6837\u5206\u5e03\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u670d\u4ece<a href=\"https:\/\/statorials.org\/cn\/\u6b63\u6001\u5206\u5e03\/\">\u6b63\u6001\u6982\u7387\u5206\u5e03<\/a>\u4e14\u5747\u503c\u4e3a<\/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-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u548c\u6807\u51c6\u5dee<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5e76\u63d0\u53d6\u5c3a\u5bf8\u6837\u672c<\/p>\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>\uff0c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u4e5f\u5c06\u7531\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\u7684\u6b63\u6001\u5206\u5e03\u5b9a\u4e49\uff1a<\/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-44571aa7337b095ab9c9fa1f746e93a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu_{\\overline{x}}=\\mu \\qquad \\sigma_{\\overline{x}}=\\cfrac{\\sigma}{\\sqrt{n}}\\\\[4ex]\\displaystyle N_{\\overline{x}}\\left(\\mu, \\frac{\\sigma}{\\sqrt{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/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-8ed084decbdfb365889aae767cf63e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u5e73\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u7684\u5e73\u5747\u503c\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9067e28d896c7e5278763081c6cc40d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u5b83\u7684\u6807\u51c6\u5dee\u3002\u6b64\u5916\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d78e2a2f2fae99a53eb087263cbb478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\sigma}{\\sqrt{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"26\" style=\"vertical-align: -16px;\"><\/p>\n<p>\u662f\u62bd\u6837\u5206\u5e03\u7684\u6807\u51c6\u8bef\u5dee\u3002<\/p>\n<p><strong>\u6ce8\uff1a<\/strong>\u5982\u679c\u603b\u4f53\u4e0d\u670d\u4ece\u6b63\u6001\u5206\u5e03\u4f46\u6837\u672c\u91cf\u8f83\u5927\uff08n&gt;30\uff09\uff0c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u4e5f\u53ef\u4ee5\u901a\u8fc7\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u903c\u8fd1\u4e4b\u524d\u7684\u6b63\u6001\u5206\u5e03\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u9075\u5faa\u6b63\u6001\u5206\u5e03\uff0c<strong>\u56e0\u6b64\u8ba1\u7b97\u4e0e\u6837\u672c\u5747\u503c\u76f8\u5173\u7684\u4efb\u4f55\u6982\u7387\u7684\u516c\u5f0f<\/strong>\u4e3a\uff1a<\/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-ecd8bcb78b739c50d01b8bad563e5cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"81\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\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-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u6837\u672c\u5747\u503c\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-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u8fd9\u662f\u4eba\u53e3\u5e73\u5747\u503c\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-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u603b\u4f53\u6807\u51c6\u5dee\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>\u662f\u6837\u672c\u5927\u5c0f\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>\u662f\u7531\u6807\u51c6\u6b63\u6001\u5206\u5e03 N(0,1) \u5b9a\u4e49\u7684\u53d8\u91cf\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-distribucion-muestral-de-la-media\"><\/span>\u5747\u503c\u62bd\u6837\u5206\u5e03\u7684\u771f\u5b9e\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u4e86\u89e3\u4e86\u5747\u503c\u62bd\u6837\u5206\u5e03\u7684\u5b9a\u4e49\u53ca\u5176\u76f8\u5173\u516c\u5f0f\u4e4b\u540e\uff0c\u8ba9\u6211\u4eec\u89e3\u51b3\u4e00\u4e2a\u793a\u4f8b\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u5927\u5b66\u751f\u7684\u4f53\u91cd\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u5e73\u5747\u503c\u4e3a 68 \u516c\u65a4\uff0c\u6807\u51c6\u5dee\u4e3a 9 \u516c\u65a4\u3002\u51b3\u5b9a\uff1a\n<ol>\n<li>\u968f\u673a\u62bd\u6837 25 \u540d\u5b66\u751f\u7684\u5e73\u5747\u503c\u5c0f\u4e8e 66 \u516c\u65a4\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<li>\u5982\u679c\u62bd\u53d6 300 \u4e2a\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c\u6709 25 \u540d\u5b66\u751f\uff0c\u90a3\u4e48\u6709\u591a\u5c11\u4e2a\u6837\u672c\u7684\u5e73\u5747\u503c\u5c0f\u4e8e 66 \u516c\u65a4\uff1f<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97\u76f8\u5e94\u7edf\u8ba1\u91cf\u7684\u503c\uff0c\u4e3a\u6b64\u6211\u4eec\u5e94\u7528\u4e0a\u9762\u770b\u5230\u7684\u516c\u5f0f\uff1a<\/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-b132f95081cac0e4028d5e8148514671_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}=\\frac{66-68}{\\displaystyle\\frac{9}{\\sqrt{25}}}=-1,11\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"238\" style=\"vertical-align: -38px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u8981\u5bfb\u627e\u7684\u6982\u7387\u5bf9\u5e94\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\u5de6\u5c3e\u7684\u503c Z=-1.11\uff0c\u53ef\u4ee5\u4ece Z \u6982\u7387\u8868\u4e2d\u8f7b\u677e\u83b7\u5f97\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4f7f\u7528 Z \u8868\u6765\u786e\u5b9a\u95ee\u9898\u5411\u6211\u4eec\u63d0\u51fa\u7684\u6982\u7387\uff1a <\/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-0db3a516f2be44a78c4f69958a9f0d51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[\\overline{x}\\leq 66]=P[Z\\leq -1,11] =0,1335\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"283\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\u89c1\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u6b63\u6001\u5206\u5e03\u8868\/\">\u8868 Z<\/a><\/div>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u968f\u673a\u6837\u672c\u7684\u5e73\u5747\u503c\u5c0f\u4e8e 66 \u516c\u65a4\u7684\u6982\u7387\uff0c\u8981\u77e5\u9053\u53d6 300 \u4e2a\u76f8\u7b49\u6837\u672c\u7684\u5e73\u5747\u503c\u5c0f\u4e8e 66 \u516c\u65a4\u7684\u6837\u672c\u6570\u91cf\uff0c\u6211\u4eec\u9700\u8981\u5c06\u8ba1\u7b97\u51fa\u7684\u6982\u7387\u4e58\u4ee5\u6240\u53d6\u6837\u672c\u603b\u6570\uff1a<\/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-7d2519cbeabf4b272e6f5a1463472768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,1335\\cdot 300 =40,05 \\approx 40\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5927\u7ea6 40 \u4e2a\u63d0\u53d6\u7684\u6837\u54c1\u7684\u5e73\u5747\u91cd\u91cf\u5c0f\u4e8e 66 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