{"id":48,"date":"2018-07-20T11:44:46","date_gmt":"2018-07-20T09:44:46","guid":{"rendered":"http:\/\/mathquiz.fr\/?page_id=48"},"modified":"2018-07-25T20:24:26","modified_gmt":"2018-07-25T18:24:26","slug":"probabilite-a-densite","status":"publish","type":"page","link":"https:\/\/mathquiz.fr\/?page_id=48","title":{"rendered":"Probabilit\u00e9 \u00e0 densit\u00e9"},"content":{"rendered":"<div id=\"mtq_quiz_area-1\" class=\"mtq_quiz_area mtq_color_blue\"> \r\n  <!--Quiz generated using mTouch Quiz Version 3.1.3 by G. Michael Guy (http:\/\/gmichaelguy.com\/quizplugin\/)-->\r\n        \r\n      \r\n  <!-- Shortcode entered mtouchquiz id=8 --> \r\n  <!-- Shortcode interpreted mtouchquiz id=8 alerts=on singlepage=on hints=off startscreen=on finalscreen=on multiplechances=off showanswers=now show_stamps=on randomq=on randoma=on status=on labels=on title=on proofread=off list=off time=off scoring=off formid= vform=on autoadvance=off autosubmit=off inform=off forcecf=off forcegf=off offset=1 questions=9 firstid=59 lastid=67 color=blue --> \r\n  <!--form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-8\"-->\r\n    <div id=\"mtq_quiztitle-1\" class=\"mtq_quiztitle\" >\r\n  <h2>Probabilit\u00e9 \u00e0 densit\u00e9<\/h2>\r\n  <\/div>\r\n      <noscript>\r\n  <div id=\"mtq_javawarning-1\" class=\"mtq_javawarning\">\r\n  Veuillez attendre la fin du chargement de l'activit\u00e9. <\/br>Si l'activit\u00e9 se ne charge pas, essayez de rafra\u00eechir votre navigateur. 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Veuillez la visiter avec Javascript activ\u00e9.  <div class=\"mtq_failed_button\" onclick=\"mtq_start_one(1)\">\r\n  Si le chargement \u00e9choue, cliquez ici pour r\u00e9-essayer  <\/div><\/div>\r\n  <\/noscript>\r\n    <div id=\"mtq_instructions-1\" class=\"mtq_instructions\"><\/div> <div id=\"mtq_start_button-1\" class='mtq_action_button mtq_css_button mtq_start_button' onclick='mtq_start_quiz(1)'> <div class=\"mtq_start_text\">\r\n  D\u00e9part  <\/div> <\/div>\r\n  <div id=\"mtq_quiz_results_bubble-1\" class=\"mtq_quiz_results_bubble\"> <div id=\"mtq_quiz_results-1\" class=\"mtq_quiz_results\"><p>F\u00e9licitation - vous avez compl\u00e9t\u00e9 <em>Probabilit\u00e9 \u00e0 densit\u00e9<\/em>.<\/p><p>Vous avez obtenu  %%SCORE%% sur %%TOTAL%%.<\/p><p>Votre performance a \u00e9t\u00e9 \u00e9valu\u00e9e \u00e0 %%RATING%%<\/p> <br>    \r\n  <\/div> <div id=\"mtq_quiz_results_highlight-1\" class=\"mtq_quiz_results_highlight\">\r\n  Vos r\u00e9ponses sont surlign\u00e9es ci-dessous.  <\/div> <\/div>\r\n    \r\n  <!-- root element for mtqscrollable -->\r\n\r\n  <div id=\"mtq_question_container-1\" style='display:none'>\r\n  <div >\r\n          <div class='mtq_question mtq_scroll_item-1' id='mtq_question-1-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 1<\/div><div id='mtq_stamp-1-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-1-1' class='mtq_question_text'>Le temps pass\u00e9 par un client, en minute, dans un supermarch\u00e9 peut \u00eatre mod\u00e9lis\u00e9 par une variable\r\nal\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> suivant la loi normale d\u2019esp\u00e9rance <span class=\"wp-katex-eq\" data-display=\"false\">\\mu = 45<\/span> et d\u2019\u00e9cart-type <span class=\"wp-katex-eq\" data-display=\"false\">\\sigma = 12<\/span>.\r\n\r\nD\u00e9terminer la valeur de <span class=\"wp-katex-eq\" data-display=\"false\">a<\/span>, arrondie \u00e0 l\u2019unit\u00e9, telle que <span class=\"wp-katex-eq\" data-display=\"false\">P(X \\leqslant a) = 0,30<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-1-1-1' onclick='mtq_button_click(1,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 1, Choice 1'>A<\/div><div id='mtq_marker-1-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">a \\approx 120,4<\/span><\/div><\/td><\/tr><tr id='mtq_row-1-2-1' onclick='mtq_button_click(1,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 1, Choice 2'>B<\/div><div id='mtq_marker-1-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">a \\approx -11,59<\/span><\/div><\/td><\/tr><tr id='mtq_row-1-3-1' onclick='mtq_button_click(1,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 1, Choice 3'>C<\/div><div id='mtq_marker-1-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">a \\approx 38,7<\/span><\/div><\/td><\/tr><tr id='mtq_row-1-4-1' onclick='mtq_button_click(1,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 1, Choice 4'>D<\/div><div id='mtq_marker-1-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">a \\approx -30,51<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-1-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 1:&nbsp;<\/div><div class='mtq_explanation-text'> On utilise la calculatrice <span class=\"wp-katex-eq\" data-display=\"false\">InvNormCD(0.3,45,12)<\/span>\r\nAinsi, <span class=\"wp-katex-eq\" data-display=\"false\">a \\approx 38,7<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-2-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 2<\/div><div id='mtq_stamp-2-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-2-1' class='mtq_question_text'>Le temps pass\u00e9 par un client, en minute, dans un supermarch\u00e9 peut \u00eatre mod\u00e9lis\u00e9 par une variable\r\nal\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> suivant la loi normale d\u2019esp\u00e9rance <span class=\"wp-katex-eq\" data-display=\"false\">\\mu = 45<\/span> et d\u2019\u00e9cart-type <span class=\"wp-katex-eq\" data-display=\"false\">\\sigma = 12<\/span>.\r\n\r\nD\u00e9terminer <span class=\"wp-katex-eq\" data-display=\"false\">P(21 \\leqslant X \\leqslant 69)<\/span> (avec solution justifi\u00e9e).<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-2-1-1' onclick='mtq_button_click(2,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 2, Choice 1'>A<\/div><div id='mtq_marker-2-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(21 \\leqslant X \\leqslant 69)\\approx 0,997<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-2-1' onclick='mtq_button_click(2,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 2, Choice 2'>B<\/div><div id='mtq_marker-2-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(21 \\leqslant X \\leqslant 69)\\approx 0,683<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-3-1' onclick='mtq_button_click(2,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 2, Choice 3'>C<\/div><div id='mtq_marker-2-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(21 \\leqslant X \\leqslant 69)=0,5<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-4-1' onclick='mtq_button_click(2,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 2, Choice 4'>D<\/div><div id='mtq_marker-2-4-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(21 \\leqslant X \\leqslant 69)\\approx 0,955<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-2-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 2:&nbsp;<\/div><div class='mtq_explanation-text'> On remarque que :\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\mu-2 \\sigma=45-2\\times12=45-24=21<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\mu+2 \\sigma=45+2\\times12=45+24=69<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nOr <span class=\"wp-katex-eq\" data-display=\"false\">P(\\mu-2 \\sigma \\leqslant X \\leqslant \\mu+2 \\sigma) \\approx 0,955 <\/span> (cf propri\u00e9t\u00e9 8.2)\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nPar cons\u00e9quent, <span class=\"wp-katex-eq\" data-display=\"false\">P(21 \\leqslant X \\leqslant 69)\\approx 0,955<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nSans justification \u00e0 la calculatrice, utiliser <span class=\"wp-katex-eq\" data-display=\"false\">NormCD(21,69,12,45)<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-3-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 3<\/div><div id='mtq_stamp-3-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-3-1' class='mtq_question_text'>Le temps pass\u00e9 par un client, en minute, dans un supermarch\u00e9 peut \u00eatre mod\u00e9lis\u00e9 par une variable\r\nal\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> suivant la loi normale d\u2019esp\u00e9rance <span class=\"wp-katex-eq\" data-display=\"false\">\\mu = 45<\/span> et d\u2019\u00e9cart-type <span class=\"wp-katex-eq\" data-display=\"false\">\\sigma = 12<\/span>.\r\n\r\nCalculer <span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)<\/span>. \r\n<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-3-1-1' onclick='mtq_button_click(3,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 3, Choice 1'>A<\/div><div id='mtq_marker-3-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)\\approx 0,122<\/span><\/div><\/td><\/tr><tr id='mtq_row-3-2-1' onclick='mtq_button_click(3,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 3, Choice 2'>B<\/div><div id='mtq_marker-3-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)\\approx 0,882<\/span><\/div><\/td><\/tr><tr id='mtq_row-3-3-1' onclick='mtq_button_click(3,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 3, Choice 3'>C<\/div><div id='mtq_marker-3-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)\\approx 0,568<\/span><\/div><\/td><\/tr><tr id='mtq_row-3-4-1' onclick='mtq_button_click(3,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 3, Choice 4'>D<\/div><div id='mtq_marker-3-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)\\approx 0,228<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-3-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 3:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)=\\dfrac{P(30\\leqslant X\\leqslant 60)}{P(X\\geqslant 30)}=\\dfrac{P(30\\leqslant X\\leqslant 60)}{1-P(X\\leqslant 30)}<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nQue l'on traduit \u00e0 la calculatrice par : <span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{NormCD(30,60,12,45)}{1-NormCD(-10^{99},30,12,45)}<\/span> ou <span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{NormCD(30,60,12,45)}{NormCD(30,10^{99},12,45)}<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nAinsi : <span class=\"wp-katex-eq\" data-display=\"false\">P_{X\\geqslant 30}(X\\leqslant 60)\\approx 0,882<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-4-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 4<\/div><div id='mtq_stamp-4-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-4-1' class='mtq_question_text'>Un supermarch\u00e9 dispose de plusieurs caisses. Un client qui se pr\u00e9sente \u00e0 une caisse doit attendre un certain temps avant d\u2019\u00eatre pris en charge par le caissier. On consid\u00e8re que ce temps d\u2019attente exprim\u00e9 en minute, par une variable al\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> qui suit la loi uniforme sur l\u2019intervalle [0; 12].\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nQuel est le temps moyen d\u2019attente \u00e0 une caisse?<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-4-1-1' onclick='mtq_button_click(4,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 4, Choice 1'>A<\/div><div id='mtq_marker-4-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-1-1' class='mtq_answer_text'>5 minutes<\/div><\/td><\/tr><tr id='mtq_row-4-2-1' onclick='mtq_button_click(4,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 4, Choice 2'>B<\/div><div id='mtq_marker-4-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-2-1' class='mtq_answer_text'>4 minutes<\/div><\/td><\/tr><tr id='mtq_row-4-3-1' onclick='mtq_button_click(4,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 4, Choice 3'>C<\/div><div id='mtq_marker-4-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-3-1' class='mtq_answer_text'>6 minutes<\/div><\/td><\/tr><tr id='mtq_row-4-4-1' onclick='mtq_button_click(4,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 4, Choice 4'>D<\/div><div id='mtq_marker-4-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-4-1' class='mtq_answer_text'>8 minutes<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-4-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 4:&nbsp;<\/div><div class='mtq_explanation-text'> On calcule l'esp\u00e9rance, comme <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> suit une loi uniforme, on a <span class=\"wp-katex-eq\" data-display=\"false\">E(X)=\\dfrac{a+b}{2}=\\dfrac{0+12}{2}=6<\/span>. (cf propri\u00e9t\u00e9 3.2)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-5-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 5<\/div><div id='mtq_stamp-5-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-5-1' class='mtq_question_text'>Le g\u00e9rant du magasin d\u00e9cide de mettre \u00e0 disposition des clients des caisses automatiques, de\r\nfa\u00e7on \u00e0 r\u00e9duire le temps d\u2019attente pour les clients ayant un panier contenant peu d\u2019articles.\r\nLe temps d\u2019attente, exprim\u00e9 en minute, \u00e0 chacune de ces caisses automatiques est mod\u00e9lis\u00e9\r\npar une variable al\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> qui suit la loi normale de moyenne 5 et d\u2019\u00e9cart type 1,5.\r\nCalculer la probabilit\u00e9 que le temps d\u2019attente \u00e0 une caisse automatique soit compris entre\r\n0,75 minute et 6 minutes.<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-5-1-1' onclick='mtq_button_click(5,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 5, Choice 1'>A<\/div><div id='mtq_marker-5-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(0,75 \\leqslant X \\leqslant 6)\\approx 0,376<\/span><\/div><\/td><\/tr><tr id='mtq_row-5-2-1' onclick='mtq_button_click(5,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 5, Choice 2'>B<\/div><div id='mtq_marker-5-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(0,75 \\leqslant X \\leqslant 6)\\approx 0,745<\/span><\/div><\/td><\/tr><tr id='mtq_row-5-3-1' onclick='mtq_button_click(5,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 5, Choice 3'>C<\/div><div id='mtq_marker-5-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(0,75 \\leqslant X \\leqslant 6)\\approx 0,642<\/span><\/div><\/td><\/tr><tr id='mtq_row-5-4-1' onclick='mtq_button_click(5,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 5, Choice 4'>D<\/div><div id='mtq_marker-5-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(0,75 \\leqslant X \\leqslant 6)\\approx 0,391<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-5-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 5:&nbsp;<\/div><div class='mtq_explanation-text'> On calcule <span class=\"wp-katex-eq\" data-display=\"false\">P(0,75 \\leqslant X \\leqslant 6)<\/span>. A la calculatrice on utilise <span class=\"wp-katex-eq\" data-display=\"false\">NormCD(0.75,6,1.5,5)<\/span>. Ainsi <span class=\"wp-katex-eq\" data-display=\"false\">P(0,75 \\leqslant X \\leqslant 6)\\approx 0,745<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-6-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 6<\/div><div id='mtq_stamp-6-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-6-1' class='mtq_question_text'>Le temps pass\u00e9 par un client, en minute, dans un supermarch\u00e9 peut \u00eatre mod\u00e9lis\u00e9 par une variable\r\nal\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> suivant la loi normale d\u2019esp\u00e9rance <span class=\"wp-katex-eq\" data-display=\"false\">\\mu = 45<\/span> et d\u2019\u00e9cart-type <span class=\"wp-katex-eq\" data-display=\"false\">\\sigma = 12<\/span>.\r\n\r\nD\u00e9terminer <span class=\"wp-katex-eq\" data-display=\"false\">P(X \\geqslant 45)<\/span> (avec solution justifi\u00e9e).<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-6-1-1' onclick='mtq_button_click(6,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 6, Choice 1'>A<\/div><div id='mtq_marker-6-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X \\geqslant 45)=0,25<\/span><\/div><\/td><\/tr><tr id='mtq_row-6-2-1' onclick='mtq_button_click(6,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 6, Choice 2'>B<\/div><div id='mtq_marker-6-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X \\geqslant 45)=0,2<\/span><\/div><\/td><\/tr><tr id='mtq_row-6-3-1' onclick='mtq_button_click(6,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 6, Choice 3'>C<\/div><div id='mtq_marker-6-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X \\geqslant 45)=0,5<\/span><\/div><\/td><\/tr><tr id='mtq_row-6-4-1' onclick='mtq_button_click(6,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 6, Choice 4'>D<\/div><div id='mtq_marker-6-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X \\geqslant 45)\\approx 0,375<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-6-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 6:&nbsp;<\/div><div class='mtq_explanation-text'> Comme <span class=\"wp-katex-eq\" data-display=\"false\">\\mu = 45<\/span>, cela implique que <span class=\"wp-katex-eq\" data-display=\"false\">P(X \\leqslant 45)=0,5<\/span> et comme la courbe est sym\u00e9trique par rapport \u00e0 la droite d'\u00e9quation <span class=\"wp-katex-eq\" data-display=\"false\">x=45<\/span>, alors <span class=\"wp-katex-eq\" data-display=\"false\">P(X \\geqslant 45)=0,5<\/span>,\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nSans justification \u00e0 la calculatrice, utiliser <span class=\"wp-katex-eq\" data-display=\"false\">NormCD(45,10^{99},12,45)<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-7-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 7<\/div><div id='mtq_stamp-7-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-7-1' class='mtq_question_text'>Un supermarch\u00e9 dispose de plusieurs caisses. Un client qui se pr\u00e9sente \u00e0 une caisse doit attendre un certain temps avant d\u2019\u00eatre pris en charge par le caissier. On consid\u00e8re que ce temps d\u2019attente exprim\u00e9 en minute, par une variable al\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> qui suit la loi uniforme sur\r\nl\u2019intervalle [0; 12].\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n\r\n\r\nQuelle est la probabilit\u00e9 qu\u2019un client attende au moins 5 minutes avant d\u2019\u00eatre pris en\r\ncharge?\r\n<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-7-1-1' onclick='mtq_button_click(7,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 7, Choice 1'>A<\/div><div id='mtq_marker-7-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{5}{12}<\/span><\/div><\/td><\/tr><tr id='mtq_row-7-2-1' onclick='mtq_button_click(7,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 7, Choice 2'>B<\/div><div id='mtq_marker-7-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{7}{12}<\/span><\/div><\/td><\/tr><tr id='mtq_row-7-3-1' onclick='mtq_button_click(7,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 7, Choice 3'>C<\/div><div id='mtq_marker-7-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{9}{12}<\/span><\/div><\/td><\/tr><tr id='mtq_row-7-4-1' onclick='mtq_button_click(7,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 7, Choice 4'>D<\/div><div id='mtq_marker-7-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{3}{12}<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-7-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 7:&nbsp;<\/div><div class='mtq_explanation-text'> Attendre au moins 5 minutes, c'est attendre 5 minutes ou plus. \r\n\r\nOn cherche donc \u00e0 calculer <span class=\"wp-katex-eq\" data-display=\"false\">P(X\\geqslant 5)<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">P(X\\geqslant 5)=1-P(X\\leqslant 5)<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">1-\\dfrac{5-0}{12-0}<\/span> (cf propri\u00e9t\u00e9 3.1)\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">1-\\dfrac{5}{12}=\\dfrac{7}{12}<\/span> <\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-8-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 8<\/div><div id='mtq_stamp-8-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-8-1' class='mtq_question_text'>Soit <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> une variable al\u00e9atoire qui suit une loi uniforme \r\nsur <span class=\"wp-katex-eq\" data-display=\"false\">[7;12]<\/span>. D\u00e9terminer la probabilit\u00e9 que <span class=\"wp-katex-eq\" data-display=\"false\">P(8\\leqslant X \\leqslant 10)<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-8-1-1' onclick='mtq_button_click(8,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 8, Choice 1'>A<\/div><div id='mtq_marker-8-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{2}{5}<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-2-1' onclick='mtq_button_click(8,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 8, Choice 2'>B<\/div><div id='mtq_marker-8-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{1}{12}<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-3-1' onclick='mtq_button_click(8,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 8, Choice 3'>C<\/div><div id='mtq_marker-8-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{2}{12}<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-4-1' onclick='mtq_button_click(8,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 8, Choice 4'>D<\/div><div id='mtq_marker-8-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{1}{5}<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-8-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 8:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">P(8\\leqslant X\\leqslant 10)=P(X\\leqslant 10)-P(X\\leqslant 8)<\/span> (cf propri\u00e9t\u00e9 1.1)\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">=\\dfrac{10-7}{12-7}-\\dfrac{8-7}{12-7}<\/span> (cf propri\u00e9t\u00e9 3.1)\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">=\\dfrac{3}{5}-\\dfrac{1}{5}=\\dfrac{2}{5}<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-9-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 9<\/div><div id='mtq_stamp-9-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-9-1' class='mtq_question_text'>Le temps pass\u00e9 par un client, en minute, dans un supermarch\u00e9 peut \u00eatre mod\u00e9lis\u00e9 par une variable\r\nal\u00e9atoire <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> suivant la loi normale d\u2019esp\u00e9rance <span class=\"wp-katex-eq\" data-display=\"false\">\\mu = 45<\/span> et d\u2019\u00e9cart-type <span class=\"wp-katex-eq\" data-display=\"false\">\\sigma = 12<\/span>.\r\n\r\nD\u00e9terminer <span class=\"wp-katex-eq\" data-display=\"false\">P(X = 10)<\/span> (avec solution justifi\u00e9e).<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-9-1-1' onclick='mtq_button_click(9,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 9, Choice 1'>A<\/div><div id='mtq_marker-9-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X = 10)=0,5<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-2-1' onclick='mtq_button_click(9,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 9, Choice 2'>B<\/div><div id='mtq_marker-9-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X = 10)=1<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-3-1' onclick='mtq_button_click(9,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 9, Choice 3'>C<\/div><div id='mtq_marker-9-3-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X = 10)=0<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-4-1' onclick='mtq_button_click(9,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 9, Choice 4'>D<\/div><div id='mtq_marker-9-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(X = 10)=0,7<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-9-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 9:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">P(X = 10)=0<\/span>, car une probabilit\u00e9 \u00e0 densit\u00e9 se calcule \u00e0 l'aide d'int\u00e9grale. Comme l'int\u00e9grale mesure l'aire sous une courbe sur un intervalle, on remarque que l'on ne peut construire aucune aire pour un seul point abscisse. (cf propri\u00e9t\u00e9 1.5)<\/div><\/div><\/div>            <div id=\"mtq_results_request-1\" class=\"mtq_results_request mtq_scroll_item-1\">\r\n        Une fois termin\u00e9, cliquez sur le bouton ci-dessous. Toutes les questions que vous n'avez pas compl\u00e9t\u00e9es sont marqu\u00e9es comme incorrectes.        <span id=\"mtq_results_button-1\" class='mtq_action_button mtq_css_button mtq_results_button'  onclick='mtq_get_results(1)'> <span class=\"mtq_results_text\">\r\n        Obtenir les r\u00e9sultats        <\/span> <\/span> <\/div>\r\n                <!--End of mtqscrollable items--> \r\n    \r\n  <\/div>\r\n  <!--End of mtqscrollable--> \r\n  <!--mtq_status-->\r\n    <div id=\"mtq_quiz_status-1\" class=\"mtq_quiz_status\">\r\n  Il y a 9 questions \u00e0 compl\u00e9ter.  <\/div>\r\n      <\/div> \r\n  <!--Holds all questions-->\r\n    <div id=\"mtq_variables\" class=\"mtq_preload\" style=\"display:none\"> <input type='hidden' id='mtq_id-1' name='mtq_id_value' value='1' \/><input type='hidden' name='question_id[]' value='66'\/><input type='hidden' id='mtq_is_answered-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-1' value='0'\/><input type='hidden' id='mtq_is_worth-1-1' 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value='0'\/><input type='hidden' id='mtq_is_correct-8-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-8-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-8-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-8-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-8-1' value='4' \/><input type='hidden' id='mtq_num_correct-8-1' value='1' \/><input type='hidden' name='question_id[]' value='63'\/><input type='hidden' id='mtq_is_answered-9-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-1' value='0'\/><input type='hidden' id='mtq_is_worth-9-1' value='100'\/><input type='hidden' id='mtq_num_attempts-9-1' value='0'\/><input type='hidden' id='mtq_points_awarded-9-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-1-1' value='0'\/><input type='hidden' id='mtq_was_selected-9-1-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-1-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-2-1' value='0'\/><input type='hidden' id='mtq_was_selected-9-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-3-1' value='1'\/><input type='hidden' id='mtq_was_selected-9-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-9-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-9-1' value='4' \/><input type='hidden' id='mtq_num_correct-9-1' value='1' \/> <div id=\"mtq_have_completed_string\" class=\"mtq_preload\">\r\n    Vous avez compl\u00e9t\u00e9    <\/div> <div id=\"mtq_questions_string\" class=\"mtq_preload\">\r\n    questions    <\/div> <div id=\"mtq_question_string\" class=\"mtq_preload\">\r\n    question    <\/div> <div id=\"mtq_your_score_is_string\"  class=\"mtq_preload\">\r\n    Votre score est de    <\/div> <div id=\"mtq_correct_string\"  class=\"mtq_preload\">\r\n    Correct    <\/div> <div id=\"mtq_wrong_string\"  class=\"mtq_preload\">\r\n    Faux    <\/div> <div id=\"mtq_partial_string\"  class=\"mtq_preload\">\r\n    R\u00e9ponse partielle    <\/div> <div id=\"mtq_exit_warning_string\"  class=\"mtq_preload\">\r\n    Vous n'avez pas fini votre quiz. Si vous quittez cette page, votre progression sera perdue.    <\/div> <div id='mtq_correct_answer_string' class='mtq_preload'>\r\n    R\u00e9ponses correctes    <\/div> <div id='mtq_you_selected_string' class='mtq_preload'>\r\n    Vous avez s\u00e9lectionn\u00e9    <\/div> <div id='mtq_not_attempted_string' class='mtq_preload'>\r\n    Pas essayer    <\/div> <div id='mtq_final_score_on_quiz_string' class='mtq_preload'>\r\n    Score final du quiz    <\/div> <div id='mtq_attempted_questions_correct_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re correcte    <\/div> <div id='mtq_attempted_questions_wrong_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re incorrecte    <\/div> <div id='mtq_questions_not_attempted_string' class='mtq_preload'>\r\n    Question non r\u00e9pondues    <\/div> <div id='mtq_total_questions_on_quiz_string' class='mtq_preload'>\r\n    Nombre total de questions dans le quiz    <\/div> <div id='mtq_question_details_string' class='mtq_preload'>\r\n    D\u00e9tail de la question    <\/div> <div id='mtq_quiz_results_string' class='mtq_preload'>\r\n    R\u00e9sultats    <\/div> <div id='mtq_date_string' class='mtq_preload'>\r\n    Date    <\/div> <div id='mtq_score_string' class='mtq_preload'>\r\n    Score    <\/div> <div id='mtq_hint_string' class='mtq_preload'>\r\n    Indice    <\/div>\r\n    <div id='mtq_time_allowed_string' class='mtq_preload'>Temps autoris\u00e9<\/div>\r\n<div id='mtq_minutes_string' class='mtq_preload'>minutes<\/div>\r\n<div id='mtq_seconds_string' class='mtq_preload'>secondes<\/div>\r\n<div id='mtq_time_used_string' class='mtq_preload'>Temps utilis\u00e9<\/div>\r\n<div id='mtq_answer_choices_selected_string' class='mtq_preload'>R\u00e9ponse(s) s\u00e9lectionn\u00e9e(s)<\/div>\r\n<div id='mtq_question_text_string' class='mtq_preload'>Texte de la question<\/div>\r\n\r\n\r\n    <input type='hidden' id='mtq_answer_display-1' value='2'\/>\r\n    <input 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name=\"mtq_max_score\" id=\"mtq_max_score-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_attempted\" id=\"mtq_questions_attempted-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_correct\" id=\"mtq_questions_correct-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_wrong\" id=\"mtq_questions_wrong-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_not_attempted\" id=\"mtq_questions_not_attempted-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" id=\"mtq_display_number-1\" value=\"1\" \/>\r\n    <input type=\"hidden\" id=\"mtq_show_list_option-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" id=\"mtq_show_stamps-1\" value=\"1\" \/>\r\n    <input type='hidden' id='mtq_num_ratings-1' value='6'\/><input type='hidden' id='mtq_ratingval-1-1' value='-1'\/><div id='mtq_rating-1-1' class='mtq_preload'>Fini<\/div><input type='hidden' id='mtq_ratingval-2-1' value='0'\/><div id='mtq_rating-2-1' class='mtq_preload'>Vous avez besoin de plus d'entra\u00eenement !<\/div><input type='hidden' id='mtq_ratingval-3-1' value='40'\/><div id='mtq_rating-3-1' class='mtq_preload'>Pers\u00e9v\u00e9rez !<\/div><input type='hidden' id='mtq_ratingval-4-1' value='60'\/><div id='mtq_rating-4-1' class='mtq_preload'>Pas mal !<\/div><input type='hidden' id='mtq_ratingval-5-1' value='80'\/><div id='mtq_rating-5-1' class='mtq_preload'>Bon travail !<\/div><input type='hidden' id='mtq_ratingval-6-1' value='100'\/><div id='mtq_rating-6-1' class='mtq_preload'>Parfait !<\/div>    <input type=\"hidden\" id=\"mtq_gf_present-1\" value=\"0\"\/>\r\n    <input type=\"hidden\" id=\"mtq_cf7_present-1\" value=\"0\"\/>\r\n    <input type=\"hidden\" id=\"mtq_quiz_in_form-1\" value=\"0\"\/>\r\n    <input type=\"hidden\" id=\"mtq_gf_formid_number-1\" value=\"\"\/>\r\n\r\n  <\/div>\r\n  \r\n  <!--Variables Div--> \r\n  <!--\/form--> \r\n<\/div>\r\n<!--Quiz area div-->\r\n\r\n\n<p><img loading=\"lazy\" class=\" 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