{"id":34386,"date":"2021-11-05T13:00:02","date_gmt":"2021-11-05T13:00:02","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34386"},"modified":"2025-09-07T23:47:57","modified_gmt":"2025-09-07T23:47:57","slug":"quomodo-distributionem-normalem-per-tabulam-computare","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/quomodo-distributionem-normalem-per-tabulam-computare\/","title":{"rendered":"Quomodo distributionem normalem per tabulam computare?"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n  <center><\/p>\n<h1>Quomodo distributionem normalem per tabulam computare?<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\">\n      <strong>Summarium<\/strong><br \/>\n      <em>In hac lectione tractabimus de distributione normali, una ex distributionibus probabilitatis continuis frequentissimis. Examinabimus quomodo variabilis aleatoria X cum parametris \u03bc et \u03c3 distributionem normalem sequi possit et quomodo haec distributio per substitutionem in integrale standardizari possit. Nihilominus animadvertimus quod, quamvis simplicatio per standardizationem fiat, calculus analytic integralium manet arduus, cum expressiones algebraicae ad exitum eius exhibendum non exsistant. Ad hoc problema superandum, tabulam distributionis normalis standardae in Excel constructam exhibebimus, quae approximationes numericas valorum functionis praebet. Explicabimus diligenter quomodo tabula adhibeatur, inclusa interpretatione probabilitatum cumulatarum tamquam arearum sub curva. Denique lectio perficitur serie exercitationum practicorum ad calculum probabilitatum et aestimationum utens tabula distributionis normalis et notione distributionis normalis standardae.<\/em>\n    <\/p>\n<p>  <\/center><br \/>\n  <\/p>\n<p style=\"text-align:center;\">\n    <strong>OBJECTIVA DISCENDI:<\/strong><br \/>\n    Post hanc lectionem, discipulus poterit:\n  <\/p>\n<ol>\n<li><strong>Demonstrare<\/strong> relationem inter distributionem normalem standardam et distributionem normalem cum parametris <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma<\/span><\/span> statutis, per substitutionem integralem.<\/li>\n<li><strong>Resolvere<\/strong> problemata practica utens tabula distributionis normalis standardae.<\/li>\n<li><strong>Construere<\/strong> atque uti tabula distributionis normalis standardae per Excel.<\/li>\n<\/ol>\n<p>  <center><br \/>\n    <strong><u>INDEX CONTENTORUM<\/u>:<\/strong><br \/>\n    <a href=\"#1\">Problema et solutio distributionis normalis<\/a><br \/>\n    <a href=\"#2\">Quomodo hac tabula utar?<\/a><br \/>\n    <a href=\"#3\">Exercitationes<\/a><br \/>\n  <\/center><br \/>\n  <center><br \/>\n    <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/GdoFK696k3s\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n  <\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Problema et solutio distributionis normalis<\/h2>\n<p style=\"text-align:justify;\">Una ex <a href=\"http:\/\/toposuranos.com\/material\/es\/distribuciones-continuas-de-probabilidad\/\" rel=\"noopener\" target=\"_blank\">distributionibus continuis<\/a> probabilitatis maxime adhibitis est distributio normalis. Variabilis aleatoria <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> distributionem normalem habet cum parametris <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu,\\sigma<\/span><\/span> si hoc valet:<\/p>\n<p class=\"eq\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(X\\leq x) =\\Phi_{\\mu,\\sigma}(x) = \\int_{-\\infty}^x \\frac{1}{\\sqrt{2\\pi}\\sigma} e^{-\\frac{1}{2} \\left(\\frac{t-\\mu}{\\sigma}\\right)^2}dt <\/span><\/span><\/p>\n<p>et etiam <a href=\"https:\/\/www.youtube.com\/watch?v=kdxgrB1h98g&amp;t=1188s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">vidimus<\/span><\/strong><\/a> hanc distributionem posse \u00abstandardizari\u00bb si in integrale substitutionem huius formae facimus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle z= \\frac{t-\\mu}{\\sigma},<\/span><\/span> obtinentes:<\/p>\n<p class=\"eq\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Phi_{\\mu,\\sigma}(x) = \\int_{-\\infty}^{\\frac{x-\\mu}{\\sigma}} \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{t^2}{2} }dt = \\Phi_{0,1}\\left(\\frac{x-\\mu}{\\sigma} \\right) <\/span><\/span><\/p>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=GdoFK696k3s&amp;t=270s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>Quamvis hic processus standardizationis<\/strong><\/span><\/a> nobis integralem simplicet, tamen non sufficit ut unam quidem probabilitatem huius distributionis computare possimus. Accidit enim ut aestimatio huius integralis analytica ratione effici non possit; revera nullae sunt expressiones algebraicae quibus exitus harum integralium exprimi possit, quod nobis difficultates affert. Nihilominus, si approximationes numericas pro aliquibus valoribus functionis distributionis normalis standardae habeamus, iam incipere possumus quasdam aestimationes efficere. Hi valores continentur in hac <strong>tabula pro distributione normali standarda<\/strong> quam in Excel pro te construxi &gt;:D<\/p>\n<p><center><br \/>\n  <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/tabla-distribucion-normalb.png\" alt=\"\" width=\"784\" height=\"774\" class=\"aligncenter size-full wp-image-26819 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/tabla-distribucion-normalb.png\" alt=\"\" width=\"784\" height=\"774\" class=\"aligncenter size-full wp-image-26819 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/tabla-distribucion-normalb.png 784w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/tabla-distribucion-normalb-300x296.png 300w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/tabla-distribucion-normalb-768x758.png 768w\" sizes=\"(max-width: 784px) 100vw, 784px\" \/><\/noscript><br \/>\n  <em>Potes hanc tabulam in forma excel deponere in hoc <a href=\"https:\/\/www.dropbox.com\/s\/9yff75b70wd75xn\/tabla%20-%20distribucion%20normal%20estandar.xlsx?dl=0\" rel=\"noopener\" target=\"_blank\">nexo.<\/a> Suadeo ut illum fasciculum recognoscas, quia sic disces tuam propriam tabulam componere, si forte nullam inveneris \ud83d\ude42<\/em><br \/>\n<\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Quomodo hac tabula utar?<\/h2>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=GdoFK696k3s&amp;t=622s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>Ut hac tabula sine difficultate uteris<\/strong><\/span><\/a> meminisse debes quod, praeterquam quod tibi probabilitatem cumulativam indicet, haec etiam repraesentat aream sub curva (functionis densitatis). Hoc in figura sequenti demonstratur:<\/p>\n<p><center><br \/>\n  <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/comousarlatablab.png\" alt=\"\" width=\"784\" height=\"774\" class=\"aligncenter size-full wp-image-26820 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/comousarlatablab.png\" alt=\"\" width=\"784\" height=\"774\" class=\"aligncenter size-full wp-image-26820 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/comousarlatablab.png 784w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/comousarlatablab-300x296.png 300w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/comousarlatablab-768x758.png 768w\" sizes=\"(max-width: 784px) 100vw, 784px\" \/><\/noscript><br \/>\n<\/center><\/p>\n<p style=\"text-align:justify;\">Hoc intellecto, sequitur ut ipsum usum tabulae exponamus. Quod hic videmus est valorem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">z<\/span><\/span> in quo functionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(z)<\/span><\/span> aestimaturi sumus in duas partes divisum apparere: in columna reperies eius expansionem usque ad primum digitum decimalem, et in ordine reperies secundum digitum decimalem; ita ut, exempli gratia: numerus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">z=1,72<\/span><\/span> inveniri possit quasi ex \u00abcoordinatis\u00bb constitutus: verticalis est <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1,7,<\/span><\/span> et horizontalis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0,02.<\/span><\/span> Denique approximatio numerica <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(1,72)<\/span><\/span> apparebit in quadrato coordinatarum \u00ab1,7\u00bb et \u00ab0,02\u00bb, quod ostendit valorem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0,957284.<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Exercitationes<\/h2>\n<ol>\n<li>Aestima valorem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(2,93)<\/span><\/span><\/li>\n<li>Aestima valorem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{\\mu=12,\\sigma=3}(11,5)<\/span><\/span><\/li>\n<li>Variabilis aleatoria <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> distributionem normalem habet <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N(\\mu=37,\\sigma=9).<\/span><\/span> Computa <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(35 \\lt X \\lt 43).<\/span><\/span><\/li>\n<li>Quantitas lycopersicorum quae quotidie in taberna mercatoris corrumpuntur habet mediam <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu=50<\/span><\/span> cum deviatone typica <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma=15.<\/span><\/span> Si mercator lycopersica ter in hebdomada portat, aestima numerum dierum quibus plus quam 60 lycopersica corrumpentur durante mense.<\/li>\n<li>Assumpto quod <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X \\sim N(\\mu,\\sigma)<\/span><\/span> computa probabilitates sequentes:\n<ol>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(\\mu - \\sigma \\leq X \\leq \\mu + \\sigma)<\/span><\/span><\/li>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X \\leq \\mu - \\sigma \\vee \\mu + \\sigma \\leq X)<\/span><\/span><\/li>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X \\leq \\mu - n\\sigma \\vee \\mu + n\\sigma \\leq X)<\/span><\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><center><br \/>\n  <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/6tEAj-_dd_c\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quomodo distributionem normalem per tabulam computare? Summarium In hac lectione tractabimus de distributione normali, una ex distributionibus probabilitatis continuis frequentissimis. Examinabimus quomodo variabilis aleatoria X cum parametris \u03bc et \u03c3 distributionem normalem sequi possit et quomodo haec distributio per substitutionem in integrale standardizari possit. Nihilominus animadvertimus quod, quamvis simplicatio per standardizationem fiat, calculus analytic integralium [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26821,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[1298,1364],"tags":[],"class_list":["post-34386","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematica","category-probabilitates-et-statistica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Quomodo distributionem normalem per tabulam computare? - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce uti tabula standardizata distributionis normalis ad probabilitates computandas et problemata practica solvenda.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/la\/quomodo-distributionem-normalem-per-tabulam-computare\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Quomodo distributionem normalem per tabulam computare?\" \/>\n<meta property=\"og:description\" content=\"Disce uti tabula standardizata distributionis normalis ad probabilitates computandas et problemata practica solvenda.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/la\/quomodo-distributionem-normalem-per-tabulam-computare\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-11-05T13:00:02+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-07T23:47:57+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/distnormal.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Quomodo distributionem normalem per tabulam computare?\" \/>\n<meta name=\"twitter:description\" content=\"Disce uti tabula standardizata distributionis normalis ad probabilitates computandas et problemata practica solvenda.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/11\/distnormal.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Quomodo distributionem normalem per tabulam computare?\",\"datePublished\":\"2021-11-05T13:00:02+00:00\",\"dateModified\":\"2025-09-07T23:47:57+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/\"},\"wordCount\":635,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/11\\\/distnormal.jpg\",\"articleSection\":[\"Mathematica\",\"Probabilitates et Statistica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/quomodo-distributionem-normalem-per-tabulam-computare\\\/\",\"name\":\"Quomodo distributionem normalem per tabulam computare? 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