{"id":6951,"date":"2011-09-30T00:40:29","date_gmt":"2011-09-29T23:40:29","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6951"},"modified":"2022-01-16T03:02:36","modified_gmt":"2022-01-16T03:02:36","slug":"um-inquerito","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6951","title":{"rendered":"Um inqu\u00e9rito"},"content":{"rendered":"<p><ul id='GTTabs_ul_6951' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6951' class='GTTabs_curr'><a  id=\"6951_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6951' ><a  id=\"6951_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6951'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6952\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6952\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4.jpg\" data-orig-size=\"301,377\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4.jpg\" class=\"alignright wp-image-6952\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4-239x300.jpg\" alt=\"\" width=\"200\" height=\"250\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4-239x300.jpg 239w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4-119x150.jpg 119w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-4.jpg 301w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Fez-se um inqu\u00e9rito aos alunos do 9.\u00ba ano da escola do Jo\u00e3o acerca do n\u00famero de irm\u00e3os.<\/p>\n<p>Os resultados est\u00e3o registados na tabela ao lado.<\/p>\n<ol>\n<li>Quantos alunos responderam ao inqu\u00e9rito?<\/li>\n<li>Elabora uma tabela de frequ\u00eancias relativas.<\/li>\n<li>Escolhendo um aluno ao acaso, qual a probabilidade de:<\/li>\n<\/ol>\n<ul>\n<li>ele ser filho \u00fanico?<\/li>\n<li>ele ter pelo menos dois irm\u00e3os?<\/li>\n<\/ul>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6951' onClick='GTTabs_show(1,6951)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6951'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como a soma das frequ\u00eancias absolutas \u00e9 $53+107+72+37+5+2=276$, responderam ao inqu\u00e9rito 276 alunos.<br \/>\n\u00ad<\/li>\n<li>\u00ad\n<\/p>\n<table class=\"aligncenter\" style=\"width: 80%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr style=\"background-color: #e9a585;\">\n<td style=\"text-align: center;\"><strong>N\u00famero de irm\u00e3os<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Freq. absoluta<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Freq. relativa simples<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Freq. relativa acumulada<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">53<\/td>\n<td style=\"text-align: center;\">$\\frac{53}{276}\\approx 0,19$<\/td>\n<td style=\"text-align: center;\">$\\frac{53}{276}\\approx 0,19$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">107<\/td>\n<td style=\"text-align: center;\">$\\frac{107}{276}\\approx 0,39$<\/td>\n<td style=\"text-align: center;\">$\\frac{160}{276}\\approx 0,58$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">2<\/td>\n<td style=\"text-align: center;\">72<\/td>\n<td style=\"text-align: center;\">$\\frac{72}{276}\\approx 0,26$<\/td>\n<td style=\"text-align: center;\">$\\frac{232}{276}\\approx 0,84$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">37<\/td>\n<td style=\"text-align: center;\">$\\frac{37}{276}\\approx 0,13$<\/td>\n<td style=\"text-align: center;\">$\\frac{269}{276}\\approx 0,97$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">4<\/td>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">$\\frac{5}{276}\\approx 0,02$<\/td>\n<td style=\"text-align: center;\">$\\frac{274}{276}\\approx 0,99$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">2<\/td>\n<td style=\"text-align: center;\">$\\frac{2}{276}\\approx 0,01$<\/td>\n<td style=\"text-align: center;\">$\\frac{276}{276}=1$<\/td>\n<\/tr>\n<tr style=\"background-color: #e9a585;\">\n<td style=\"text-align: center;\"><strong>TOTAL<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>276<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>\u00a01<\/strong><\/td>\n<td style=\"text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Escolhendo um aluno ao acaso,<\/li>\n<\/ol>\n<ul>\n<li>a probabilidade de ele ser filho \u00fanico \u00e9 $P=\\frac{53}{276}\\approx 0,19$;<\/li>\n<li>a probabilidade de ele ter pelo menos dois irm\u00e3os \u00e9 $P=\\frac{72+37+5+2}{276}=\\frac{116}{276}\\approx 0,42$.<\/li>\n<\/ul>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6951' onClick='GTTabs_show(0,6951)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Fez-se um inqu\u00e9rito aos alunos do 9.\u00ba ano da escola do Jo\u00e3o acerca do n\u00famero de irm\u00e3os. Os resultados est\u00e3o registados na tabela ao lado. Quantos alunos responderam ao inqu\u00e9rito? Elabora&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20344,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,219,222,215],"series":[],"class_list":["post-6951","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-estatistica-e-probabilidades","tag-9-o-ano","tag-estatistica-2","tag-frequencia-relativa","tag-probabilidade"],"views":2122,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9V1Pag027-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6951","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6951"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6951\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20344"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6951"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6951"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6951"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6951"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}