{"id":11706,"date":"2026-06-25T14:45:11","date_gmt":"2026-06-25T12:45:11","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=11706"},"modified":"2026-06-25T14:57:54","modified_gmt":"2026-06-25T12:57:54","slug":"estimation-du-cout-des-courses-et-theoreme-central-limit","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2026\/06\/25\/estimation-du-cout-des-courses-et-theoreme-central-limit\/","title":{"rendered":"Estimation du co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Comment effectuer une estimation du co\u00fbt des courses \u00e0 l&rsquo;aide du th\u00e9or\u00e8me central limit ? En arrondissant \u00e0 l&rsquo;entier le prix de chaque article, on peut en effet avoir une id\u00e9e du montant total de nos achats.<\/p>\n\n\n\n<!--more-->\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a8da921857ab&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a8da921857ab\" class=\"aligncenter size-medium wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2026\/06\/Courses-theoreme-central-limit-300x200.png\" alt=\"courses th\u00e9or\u00e8me central limit\" class=\"wp-image-11707\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2026\/06\/Courses-theoreme-central-limit-300x200.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2026\/06\/Courses-theoreme-central-limit-1024x683.png 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2026\/06\/Courses-theoreme-central-limit-768x512.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2026\/06\/Courses-theoreme-central-limit-360x240.png 360w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2026\/06\/Courses-theoreme-central-limit.png 1536w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2026\/06\/25\/estimation-du-cout-des-courses-et-theoreme-central-limit\/#Cout_des_courses_et_Theoreme_Central_Limit_un_exemple\" >Co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit: un exemple<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2026\/06\/25\/estimation-du-cout-des-courses-et-theoreme-central-limit\/#Cout_des_courses_et_Theoreme_Central_Limit_explications\" >Co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit: explications<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2026\/06\/25\/estimation-du-cout-des-courses-et-theoreme-central-limit\/#Somme_de_variables_aleatoires_independantes\" >Somme de variables al\u00e9atoires ind\u00e9pendantes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2026\/06\/25\/estimation-du-cout-des-courses-et-theoreme-central-limit\/#Mais_ou_est_le_Theoreme_Central_Limit_TCL_dans_tout_ca\" >Mais o\u00f9 est le Th\u00e9or\u00e8me Central Limit (TCL) dans tout \u00e7a ?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cout_des_courses_et_Theoreme_Central_Limit_un_exemple\"><\/span>Co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit: un exemple<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Avec les scannettes, vous n&rsquo;aurez pas besoin de cette astuce car elle vous donne le prix total au fur et \u00e0 mesure. Alors, imaginez que vous pr\u00e9pariez la liste de vos courses. Vous n&rsquo;avez pas le prix exact de chaque article, mais uniquement un ordre de grandeur \u00e0 l&rsquo;euro pr\u00e8s. \u00c0 chaque article que vous inscrivez, vous ajoutez l&rsquo;arrondi \u00e0 l&rsquo;unit\u00e9 de son prix (tant\u00f4t sup\u00e9rieur, tant\u00f4t inf\u00e9rieur).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Imaginez que vous avez 30 articles sur votre liste.<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msqrt><mn>30<\/mn><\/msqrt><mo>=<\/mo><msqrt><mrow><mn>25<\/mn><mo>+<\/mo><mn>5<\/mn><\/mrow><\/msqrt><mo>=<\/mo><msqrt><mrow><mn>25<\/mn><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>5<\/mn><mn>25<\/mn><\/mfrac><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><\/mrow><\/msqrt><mo>=<\/mo><mn>5<\/mn><msqrt><mrow><mn>1<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><\/mrow><\/msqrt><mo>\u2248<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>15<\/mn><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>\u2248<\/mo><mn>5,5.<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{30}=\\sqrt{25+5}=\\sqrt{25\\left(1+\\frac{5}{25}\\right)}=5\\sqrt{1+\\frac{1}{5}}\\approx5\\times\\left(1+\\frac{1}{2}\\times{1}{5}\\right)\\approx5,5.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">J&rsquo;ai ici utilis\u00e9 une approximation affine:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msqrt><mrow><mn>1<\/mn><mo>+<\/mo><mi>x<\/mi><\/mrow><\/msqrt><mo>\u2248<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{1+x}\\approx1+\\frac{1}{2}x<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Maintenant, on multiplie par 0,3 ce dernier r\u00e9sultat:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mn>5,5<\/mn><mo>\u00d7<\/mo><mn>0,3<\/mn><mo>=<\/mo><mn>1,65.<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5,5 \\times 0,3 = 1,65.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Alors, la somme totale que vous avez obtenue en additionnant les arrondis diff\u00e8rent de 1,65 \u20ac du montant r\u00e9el.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Certains prennent 0,25 \u00e0 la place de 0,3 (pour faciliter les calculs), mais c&rsquo;est l\u00e9g\u00e8rement moins pr\u00e9cis (m\u00eame si cela donne un bon ordre de grandeur pour ce que nous calculons &#8211; ici, on trouverait 1,375 \u00e0 la place de 1,65).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cout_des_courses_et_Theoreme_Central_Limit_explications\"><\/span>Co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit: explications<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Ceci est en relation avec le programme de Terminale, enseignement de Sp\u00e9cialit\u00e9, mais le d\u00e9passe car nous allons parler de lois de probabilit\u00e9s continues.<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Somme_de_variables_aleatoires_independantes\"><\/span>Somme de variables al\u00e9atoires ind\u00e9pendantes<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Notons :<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mo>\u22ef<\/mo><mspace width=\"0.1667em\"><\/mspace><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><msub><mi>X<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">X_1,\\ X_2,\\ \\cdots,\\ X_n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">les <em>n<\/em> variables al\u00e9atoires (V.A.) repr\u00e9sentant la diff\u00e9rence de prix entre l&rsquo;arrondi choisi et le prix r\u00e9el des <em>n<\/em> articles achet\u00e9s.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ces variables al\u00e9atoires sont ind\u00e9pendantes donc la variance de leur somme est la somme de leurs variances:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mo>\u22ef<\/mo><mo>+<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mo>\u22ef<\/mo><mo>+<\/mo><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V(X_1+X_2+\\cdots+X_n)=V(X_1)+V(X_2)+\\cdots+V(X_n).<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Chaque V.A. suit la loi uniforme sur [-0,5 ; 0,5]. En effet, les centimes peuvent \u00eatre mis al\u00e9atoirement de mani\u00e8re quasi-continue sur cet intervalle. QAinsi, la variance de chaque V.A. est \u00e9gale \u00e0:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>k<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mn>0<\/mn><mo separator=\"true\">,<\/mo><msup><mn>5<\/mn><mn>2<\/mn><\/msup><\/mrow><mn>3<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>12<\/mn><\/mfrac><mo>\u2248<\/mo><mn>0,0833.<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">V(X_k)=\\frac{0,5^2}{3}=\\frac{1}{12}\\approx0,0833.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Quant \u00e0 l&rsquo;esp\u00e9rance, elle est \u00e9gale \u00e0:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>k<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mo lspace=\"0em\" rspace=\"0em\">\u2212<\/mo><mn>0,5<\/mn><mo>+<\/mo><mn>0,5<\/mn><\/mrow><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0.<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">E(X_k)=\\frac{-0,5+0,5}{2}=0.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Posons:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><msub><mi>S<\/mi><mi>n<\/mi><\/msub><mo>=<\/mo><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mo>\u22ef<\/mo><mo>+<\/mo><msub><mi>X<\/mi><mi>n<\/mi><\/msub><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S_n=X_1+X_2+\\cdots+X_n.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">On a alors:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>S<\/mi><mi>n<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>k<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>k<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">E(S_n)=\\sum_{k=1}^n E(X_k)=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">par lin\u00e9arit\u00e9 de l&rsquo;esp\u00e9rance, et:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>S<\/mi><mi>n<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>k<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>k<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0,0833<\/mn><mi>n<\/mi><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V(S_n)=\\sum_{k=1}^n V(X_k)=0,0833n.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">car les V.A. sont ind\u00e9pendantes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On en d\u00e9duit alors que l&rsquo;\u00e9cart-type est:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03c3<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>S<\/mi><mi>n<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msqrt><mrow><mi>V<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>S<\/mi><mi>n<\/mi><\/msub><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><mo>\u2248<\/mo><mn>0,3<\/mn><msqrt><mi>n<\/mi><\/msqrt><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma(S_n)=\\sqrt{V(S_n)}\\approx0,3\\sqrt{n}.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">On arrive alors \u00e0 la formule que nous avons appliqu\u00e9 dans l&rsquo;exemple de la section pr\u00e9c\u00e9dente.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mais_ou_est_le_Theoreme_Central_Limit_TCL_dans_tout_ca\"><\/span>Mais o\u00f9 est le Th\u00e9or\u00e8me Central Limit (TCL) dans tout \u00e7a ?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Tr\u00e8s bonne question, et je me f\u00e9licite de l&rsquo;avoir pos\u00e9. En effet, nous n&rsquo;avons pas encore parl\u00e9 du TCL.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Le TCL stipule que la variable al\u00e9atoire \u00ab\u00a0Somme\u00a0\u00bb se comporte comme une V.A. suivant la loi normale d&rsquo;esp\u00e9rance 0 et de variance 1\/12.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ainsi, pour 30 articles, l&rsquo;\u00e9cart-type est: <\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><msqrt><mfrac><mn>30<\/mn><mn>12<\/mn><\/mfrac><\/msqrt><mo>=<\/mo><msqrt><mn>2,5<\/mn><\/msqrt><mo>\u2248<\/mo><mn>1,58.<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma=\\sqrt{\\frac{30}{12}}=\\sqrt{2,5}\\approx1,58.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Dans un cas g\u00e9n\u00e9ral, l&rsquo;\u00e9cart-type est:<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mfrac><msqrt><mi>n<\/mi><\/msqrt><msqrt><mn>12<\/mn><\/msqrt><\/mfrac><mo>\u2248<\/mo><mn>0,3<\/mn><msqrt><mi>n<\/mi><\/msqrt><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma=\\frac{\\sqrt{n}}{\\sqrt{12}}\\approx0,3\\sqrt{n}.<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">On obtient alors la m\u00eame formule que pr\u00e9c\u00e9demment.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Comment effectuer une estimation du co\u00fbt des courses \u00e0 l&rsquo;aide du th\u00e9or\u00e8me central limit ? En arrondissant \u00e0 l&rsquo;entier le prix de chaque article, on peut en effet avoir une id\u00e9e du montant total de nos achats.<\/p>\n","protected":false},"author":1,"featured_media":11708,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[169],"class_list":["post-11706","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","tag-probabilites"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Estimation du co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit - Mathweb.fr<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.mathweb.fr\/euclide\/2026\/06\/25\/estimation-du-cout-des-courses-et-theoreme-central-limit\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Estimation du co\u00fbt des courses et Th\u00e9or\u00e8me Central Limit - Mathweb.fr\" \/>\n<meta property=\"og:description\" content=\"Comment effectuer une estimation du co\u00fbt des courses \u00e0 l&rsquo;aide du th\u00e9or\u00e8me central limit ? 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