{"id":274,"date":"2023-08-03T05:14:26","date_gmt":"2023-08-03T05:14:26","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d1%80%d0%be%d0%b7%d0%bf%d0%be%d0%b4%d1%96%d0%bb-%d0%bf%d1%80%d0%be%d0%bf%d0%be%d1%80%d1%86%d1%96%d1%96-%d0%b2%d0%b8%d0%b1%d1%96%d1%80%d0%ba%d0%b8\/"},"modified":"2023-08-03T05:14:26","modified_gmt":"2023-08-03T05:14:26","slug":"%d1%80%d0%be%d0%b7%d0%bf%d0%be%d0%b4%d1%96%d0%bb-%d0%bf%d1%80%d0%be%d0%bf%d0%be%d1%80%d1%86%d1%96%d1%96-%d0%b2%d0%b8%d0%b1%d1%96%d1%80%d0%ba%d0%b8","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d1%80%d0%be%d0%b7%d0%bf%d0%be%d0%b4%d1%96%d0%bb-%d0%bf%d1%80%d0%be%d0%bf%d0%be%d1%80%d1%86%d1%96%d1%96-%d0%b2%d0%b8%d0%b1%d1%96%d1%80%d0%ba%d0%b8\/","title":{"rendered":"\u0412\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0447\u0430\u0441\u0442\u043a\u0438"},"content":{"rendered":"<p>\u0423 \u0446\u0456\u0439 \u0441\u0442\u0430\u0442\u0442\u0456 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u0442\u044c\u0441\u044f, \u0449\u043e \u0442\u0430\u043a\u0435 \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0447\u0430\u0441\u0442\u043a\u0438 \u0432 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0446\u0456. \u0422\u0430\u043a \u0441\u0430\u043c\u043e \u0432\u0438 \u0437\u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439\u043d\u043e\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u0442\u0430, \u043a\u0440\u0456\u043c \u0442\u043e\u0433\u043e, \u043f\u043e\u043a\u0440\u043e\u043a\u043e\u0432\u0443 \u0432\u043f\u0440\u0430\u0432\u0443. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral-de-la-proporcion\"><\/span> \u042f\u043a\u0438\u0439 \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0447\u0430\u0441\u0442\u043a\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0412\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439<\/strong> (\u0430\u0431\u043e <strong>\u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439<\/strong> ) \u2014 \u0446\u0435 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b, \u044f\u043a\u0438\u0439 \u0454 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f \u0447\u0430\u0441\u0442\u043a\u0438 \u043a\u043e\u0436\u043d\u043e\u0457 \u043c\u043e\u0436\u043b\u0438\u0432\u043e\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u0456\u0437 \u0441\u0443\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0456. \u0422\u043e\u0431\u0442\u043e <a href=\"https:\/\/statorials.org\/uk\/\u0447\u0430\u0441\u0442\u043a\u0430-\u0437\u0440\u0430\u0437\u043a\u0430\/\">\u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438<\/a> \u0432\u0441\u0456\u0445 \u043c\u043e\u0436\u043b\u0438\u0432\u0438\u0445 \u0432\u0438\u0431\u0456\u0440\u043e\u043a \u0456\u0437 \u0433\u0435\u043d\u0435\u0440\u0430\u043b\u044c\u043d\u043e\u0457 \u0441\u0443\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0456 \u0443\u0442\u0432\u043e\u0440\u044e\u044e\u0442\u044c \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0457.<\/p>\n<p> \u0406\u043d\u0448\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439\u043d\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u0432\u0438\u0445\u043e\u0434\u0438\u0442\u044c \u0448\u043b\u044f\u0445\u043e\u043c \u0432\u0438\u0432\u0447\u0435\u043d\u043d\u044f \u0432\u0441\u0456\u0445 \u0432\u0438\u0431\u0456\u0440\u043e\u043a, \u044f\u043a\u0456 \u043c\u043e\u0436\u043d\u0430 \u0432\u0456\u0434\u0456\u0431\u0440\u0430\u0442\u0438 \u0437 \u0433\u0435\u043d\u0435\u0440\u0430\u043b\u044c\u043d\u043e\u0457 \u0441\u0443\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0456, \u0456 \u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0447\u0430\u0441\u0442\u043a\u0438 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u0434\u043b\u044f \u043a\u043e\u0436\u043d\u043e\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438. \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, \u043d\u0430\u0431\u0456\u0440 \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0445 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0457.<\/p>\n<p> \u042f\u043a\u0449\u043e \u0432\u0430\u043c \u0446\u0456\u043a\u0430\u0432\u043e, \u0434\u043b\u044f \u0447\u043e\u0433\u043e \u043f\u0440\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0457, \u0443 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0446\u0456 \u0432\u0456\u043d \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0454\u0442\u044c\u0441\u044f \u0434\u043b\u044f \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u043e\u0441\u0442\u0456 \u043d\u0430\u0431\u043b\u0438\u0436\u0435\u043d\u043d\u044f \u0434\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0457 \u0433\u0435\u043d\u0435\u0440\u0430\u043b\u044c\u043d\u043e\u0457 \u0441\u0443\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0456 \u043f\u0456\u0434 \u0447\u0430\u0441 \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u043e\u0434\u043d\u0456\u0454\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438. <\/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>\u0414\u0438\u0432.:<\/strong> <a href=\"https:\/\/statorials.org\/uk\/\u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0438-\u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b-\u0441\u0435\u0440\u0435\u0434\u043d\u044c\u043e\u0433\u043e\/\">\u0412\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0441\u0435\u0440\u0435\u0434\u043d\u044c\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-proporcion\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439\u043d\u043e\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0424\u0430\u043a\u0442\u0438\u0447\u043d\u043e, \u043a\u043e\u043b\u0438 \u043c\u0438 \u0432\u0438\u0432\u0447\u0430\u0454\u043c\u043e \u0447\u0430\u0441\u0442\u043a\u0443 \u0432\u0438\u0431\u0456\u0440\u043a\u0438, \u043c\u0438 \u0430\u043d\u0430\u043b\u0456\u0437\u0443\u0454\u043c\u043e \u0432\u0438\u043f\u0430\u0434\u043a\u0438 \u0443\u0441\u043f\u0456\u0445\u0443. \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, \u0432\u0438\u043f\u0430\u0434\u043a\u043e\u0432\u0430 \u0437\u043c\u0456\u043d\u043d\u0430 \u0432 \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043d\u0456 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0454 <a href=\"https:\/\/statorials.org\/uk\/\u0431\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0438\u0438-\u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b-1\/\">\u0431\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u043e\u043c\u0443 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u043e\u0441\u0442\u0435\u0439<\/a> .<\/p>\n<p> \u0412\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u043e \u0434\u043e \u0446\u0435\u043d\u0442\u0440\u0430\u043b\u044c\u043d\u043e\u0457 \u0433\u0440\u0430\u043d\u0438\u0447\u043d\u043e\u0457 \u0442\u0435\u043e\u0440\u0435\u043c\u0438, \u0434\u043b\u044f \u0432\u0435\u043b\u0438\u043a\u0438\u0445 \u0440\u043e\u0437\u043c\u0456\u0440\u0456\u0432 (n&gt;30) \u043c\u0438 \u043c\u043e\u0436\u0435\u043c\u043e \u043d\u0430\u0431\u043b\u0438\u0437\u0438\u0442\u0438 \u0431\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0434\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e. \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, <strong>\u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0447\u0430\u0441\u0442\u043a\u0438 \u043d\u0430\u0431\u043b\u0438\u0436\u0430\u0454\u0442\u044c\u0441\u044f \u0434\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u0437 \u0442\u0430\u043a\u0438\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438:<\/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> \u0437\u043e\u043b\u043e\u0442\u043e<\/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> \u0446\u0435 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u0443\u0441\u043f\u0456\u0445\u0443 \u0456<\/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> \u0446\u0435 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u043d\u0435\u0432\u0434\u0430\u0447\u0456<\/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> .<\/p>\n<p> <strong>\u041f\u0440\u0438\u043c\u0456\u0442\u043a\u0430.<\/strong> \u0411\u0456\u043d\u043e\u043c\u0456\u0430\u043b\u044c\u043d\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043c\u043e\u0436\u043d\u0430 \u043d\u0430\u0431\u043b\u0438\u0437\u0438\u0442\u0438 \u0434\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e, \u043b\u0438\u0448\u0435 \u044f\u043a\u0449\u043e<\/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> ,<\/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> \u0406<\/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> . <\/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>\u0414\u0438\u0432.:<\/strong> <a href=\"https:\/\/statorials.org\/uk\/\u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u0438\u0438-\u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\/\">\u041f\u0440\u0438\u043a\u043b\u0430\u0434\u0438 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443<\/a><\/div>\n<p> \u041e\u0442\u0436\u0435, \u043e\u0441\u043a\u0456\u043b\u044c\u043a\u0438 \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u0447\u0430\u0441\u0442\u043a\u0438 \u043c\u043e\u0436\u043d\u0430 \u043d\u0430\u0431\u043b\u0438\u0437\u0438\u0442\u0438 \u0434\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443, <strong>\u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0434\u043b\u044f \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443 \u0431\u0443\u0434\u044c-\u044f\u043a\u043e\u0457 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u043e\u0441\u0442\u0456, \u043f\u043e\u0432\u2019\u044f\u0437\u0430\u043d\u043e\u0457 \u0437 \u0447\u0430\u0441\u0442\u043a\u043e\u044e \u0432\u0438\u0431\u0456\u0440\u043a\u0438,<\/strong> \u043c\u0430\u0454 \u0432\u0438\u0433\u043b\u044f\u0434:<\/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\"> \u0437\u043e\u043b\u043e\u0442\u043e:<\/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> \u0454 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0454\u044e \u0437\u0440\u0430\u0437\u043a\u0430.<\/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> \u0446\u0435 \u0447\u0430\u0441\u0442\u043a\u0430 \u043d\u0430\u0441\u0435\u043b\u0435\u043d\u043d\u044f.<\/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> \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u0432\u0456\u0434\u043c\u043e\u0432\u0438 \u043f\u043e\u043f\u0443\u043b\u044f\u0446\u0456\u0457,<\/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> .<\/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> \u0446\u0435 \u0440\u043e\u0437\u043c\u0456\u0440 \u0432\u0438\u0431\u0456\u0440\u043a\u0438.<\/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> \u0454 \u0437\u043c\u0456\u043d\u043d\u043e\u044e, \u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043e\u044e \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u0438\u043c \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u0438\u043c \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u043e\u043c N(0,1). <\/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> \u041a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434 \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439\u043d\u043e\u0433\u043e \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u0432\u0438\u0431\u0456\u0440\u043a\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u0456\u0441\u043b\u044f \u0442\u043e\u0433\u043e, \u044f\u043a \u043c\u0438 \u043e\u0437\u043d\u0430\u0439\u043e\u043c\u0438\u043b\u0438\u0441\u044f \u0437 \u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f\u043c \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439\u043d\u043e\u0433\u043e \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u043e\u0433\u043e \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443 \u0442\u0430 \u043f\u043e\u0432\u2019\u044f\u0437\u0430\u043d\u0438\u043c\u0438 \u0437 \u043d\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438, \u043d\u0438\u0436\u0447\u0435 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u043e \u043f\u043e\u043a\u0440\u043e\u043a\u043e\u0432\u0438\u0439 \u043f\u0440\u0438\u043a\u043b\u0430\u0434 \u0432\u0438\u0440\u0456\u0448\u0435\u043d\u043d\u044f, \u0449\u043e\u0431 \u043f\u043e\u0432\u043d\u0456\u0441\u0442\u044e \u0437\u0440\u043e\u0437\u0443\u043c\u0456\u0442\u0438 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0456\u044e.<\/p>\n<ul>\n<li> \u041f\u0440\u043e\u043c\u0438\u0441\u043b\u043e\u0432\u0430 \u043a\u043e\u043c\u043f\u0430\u043d\u0456\u044f \u043a\u0443\u043f\u0443\u0454 \u043f\u0430\u0440\u0442\u0456\u0457 \u0434\u0435\u0442\u0430\u043b\u0435\u0439 \u043d\u0430 \u0437\u0430\u0432\u043e\u0434\u0456, \u044f\u043a\u0438\u0439 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043e \u0432\u0438\u0440\u043e\u0431\u043b\u044f\u0454 \u0434\u0435\u0442\u0430\u043b\u0456 \u043b\u0438\u0448\u0435 \u0437 3% \u0431\u0440\u0430\u043a\u043e\u0432\u0430\u043d\u0438\u0445 \u0434\u0435\u0442\u0430\u043b\u0435\u0439. \u0429\u043e\u0431 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u0438\u0442\u0438 \u0446\u0435, \u043a\u043e\u043c\u043f\u0430\u043d\u0456\u044f \u0432\u0438\u0440\u0456\u0448\u0443\u0454 \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0456\u0437\u0443\u0432\u0430\u0442\u0438 \u0437\u0430\u043c\u043e\u0432\u043b\u0435\u043d\u043d\u044f \u0437 500 \u0434\u0435\u0442\u0430\u043b\u0435\u0439. \u042f\u043a\u0430 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u0432\u0438\u044f\u0432\u043b\u0435\u043d\u043d\u044f \u0443 \u0437\u0440\u0430\u0437\u043a\u0443 \u0431\u0456\u043b\u044c\u0448\u0435 5% \u0431\u0440\u0430\u043a\u043e\u0432\u0430\u043d\u0438\u0445 \u0434\u0435\u0442\u0430\u043b\u0435\u0439?<\/li>\n<\/ul>\n<p> \u0423 \u0446\u044c\u043e\u043c\u0443 \u0432\u0438\u043f\u0430\u0434\u043a\u0443 \u0447\u0430\u0441\u0442\u043a\u0430 \u043d\u0430\u0441\u0435\u043b\u0435\u043d\u043d\u044f, \u044f\u043a\u0443 \u043c\u0438 \u0445\u043e\u0447\u0435\u043c\u043e \u0432\u0438\u0432\u0447\u0438\u0442\u0438, \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c 0,03, \u0442\u043e\u043c\u0443 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 q \u0435\u043a\u0432\u0456\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0438\u0439 0,97.<\/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> \u041e\u0442\u0436\u0435, \u0449\u043e\u0431 \u0437\u043d\u0430\u0439\u0442\u0438 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0449\u043e \u0432\u043e\u043d\u0438 \u0437\u0430\u043f\u0438\u0442\u0443\u044e\u0442\u044c \u043d\u0430\u0441, \u043c\u0438 \u043f\u043e\u0432\u0438\u043d\u043d\u0456 \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u0443 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0443, \u0437\u0430\u0441\u0442\u043e\u0441\u0443\u0432\u0430\u0432\u0448\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u044f\u043a\u0443 \u043c\u0438 \u0431\u0430\u0447\u0438\u043b\u0438 \u0432 \u043f\u043e\u043f\u0435\u0440\u0435\u0434\u043d\u044c\u043e\u043c\u0443 \u0440\u043e\u0437\u0434\u0456\u043b\u0456:<\/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\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}=\\cfrac{0,05-0,03}{\\displaystyle\\sqrt{\\frac{0,03\\cdot 0,97}{500}}}=2,62\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"264\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u043e\u0442\u0440\u0438\u043c\u0430\u0442\u0438 \u0431\u0456\u043b\u044c\u0448\u0435 5% \u0431\u0440\u0430\u043a\u043e\u0432\u0430\u043d\u0438\u0445 \u0434\u0435\u0442\u0430\u043b\u0435\u0439 \u0435\u043a\u0432\u0456\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u0442\u0430\u043a\u0456\u0439 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u043e\u0441\u0442\u0456:<\/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-a5e5cff61f2cc97762df561b3e35a7ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\\left[\\widehat{p}>0,05\\right]=P[Z>2,62]=1-P[Z\\leq 2,62]&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;360&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> \u041d\u0430\u0440\u0435\u0448\u0442\u0456, \u043c\u0438 \u0448\u0443\u043a\u0430\u0454\u043c\u043e \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c P[Z\u22642,62] \u0443 <a href=\"https:\/\/statorials.org\/uk\/\u0442\u0430\u0431\u043b\u0438\u0446\u044f-\u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e-\u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443\/\">\u0442\u0430\u0431\u043b\u0438\u0446\u0456 Z-\u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b\u0443<\/a> \u0442\u0430 \u043e\u0431\u0447\u0438\u0441\u043b\u044e\u0454\u043c\u043e \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c, \u044f\u043a\u0443 \u0437\u0430\u043f\u0438\u0442\u0443\u0454 \u043d\u0430\u0441 \u0437\u0430\u0434\u0430\u0447\u0430:<\/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> \u041f\u0456\u0434\u0441\u0443\u043c\u043e\u0432\u0443\u044e\u0447\u0438, \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c \u0432\u0438\u044f\u0432\u043b\u0435\u043d\u043d\u044f \u0431\u0456\u043b\u044c\u0448\u0435 5% \u0434\u0435\u0444\u0435\u043a\u0442\u043d\u0438\u0445 \u0434\u0435\u0442\u0430\u043b\u0435\u0439 \u0432 \u0430\u043d\u0430\u043b\u0456\u0437\u043e\u0432\u0430\u043d\u043e\u043c\u0443 \u0437\u0440\u0430\u0437\u043a\u0443 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c 0,44%.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0423 \u0446\u0456\u0439 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\u0447\u0430\u0441\u0442\u043a\u0438? \u0412\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439 (\u0430\u0431\u043e \u0432\u0438\u0431\u0456\u0440\u043a\u043e\u0432\u0438\u0439 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0439 ) \u2014 \u0446\u0435 \u0440\u043e\u0437\u043f\u043e\u0434\u0456\u043b, \u044f\u043a\u0438\u0439 \u0454 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f \u0447\u0430\u0441\u0442\u043a\u0438 \u043a\u043e\u0436\u043d\u043e\u0457 \u043c\u043e\u0436\u043b\u0438\u0432\u043e\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 \u0456\u0437 \u0441\u0443\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u0456. \u0422\u043e\u0431\u0442\u043e \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0456\u0457 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 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