{"id":448,"date":"2023-07-29T21:10:12","date_gmt":"2023-07-29T21:10:12","guid":{"rendered":"https:\/\/statorials.org\/pt\/problemas-empiricos-de-regras-praticas\/"},"modified":"2023-07-29T21:10:12","modified_gmt":"2023-07-29T21:10:12","slug":"problemas-empiricos-de-regras-praticas","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/problemas-empiricos-de-regras-praticas\/","title":{"rendered":"Problemas na pr\u00e1tica de regras pr\u00e1ticas"},"content":{"rendered":"<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>h1 {\ncolor: black;\ntext-align: center;\nmargin-top: 15px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>h2 {\ncolor: black;\nfont-size: 20px;\ntext-align: center;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>p {\ncolor: black;\ntext-align: center;\nmargin-bottom: 15px;\nmargin-top: 15px;\nfont-family: 'Raleway', sans-serif;\n}<\/p>\n<p>#words_intro {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#solution_div {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_output {\ntext-align: center;\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words_outro {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\n}<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#calcTitle {\ntext-align: center;\nfont-size: 20px;\nmargin-bottom: 0px;\nfont-family: 'Raleway', serif;\n}<\/p>\n<p>#hr_top {\nwidth: 70%;\nmargin-bottom: 15px;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>#hr_bottom {\nwidth: 30%;\nmargin-top: 15px;\nborder: none;\nheight: 2px;\ncolor: black;\nbackground-color: black;\n}<\/p>\n<p>.input_label_calc {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button_calc {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;\n      padding: 10px 10px;\n      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #button_calc:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>\t    .label_radio {\n\ttext-align: center;\n}\n<\/style>\n<div id=\"words_intro\">A <b>regra pr\u00e1tica<\/b> , \u00e0s vezes chamada de regra 68-95-99,7, afirma que para um determinado conjunto de dados com distribui\u00e7\u00e3o normal:<\/div>\n<div id=\"words_intro\"> <b>68%<\/b> dos valores dos dados est\u00e3o dentro de um desvio padr\u00e3o da m\u00e9dia.<\/div>\n<div id=\"words_intro\"> <b>95%<\/b> dos valores dos dados est\u00e3o dentro de dois desvios padr\u00e3o da m\u00e9dia.<\/div>\n<div id=\"words_intro\"> <b>99,7%<\/b> dos valores dos dados est\u00e3o dentro de tr\u00eas desvios padr\u00e3o da m\u00e9dia.<\/div>\n<div id=\"words_intro\"> Teste seu conhecimento da regra pr\u00e1tica usando os problemas pr\u00e1ticos abaixo.<\/div>\n<hr id=\"hr_top\">\n<div id=\"words_intro\"> A altura das plantas em um determinado jardim \u00e9 normalmente distribu\u00edda com uma m\u00e9dia de <span id=\"mean\">12,3<\/span> polegadas e um desvio padr\u00e3o de <span id=\"sd\">4,1<\/span> polegadas.<\/div>\n<div id=\"words_intro\"> <b>Use a regra pr\u00e1tica para estimar a porcentagem de plantas que t\u00eam <span id=\"scenario\">entre 8,2 e 16,4<\/span> polegadas de altura.<\/b><\/div>\n<div id=\"words\"><input class=\"input_label_calc\" type=\"number\" id=\"answer\" value=\"\"> % <\/div>\n<div id=\"words\"><input class=\"input_label_calc\" type=\"button\" id=\"button_calc\" onclick=\"check()\" value=\"Check Answer\"><\/div>\n<div id=\"words_output\"><b><span id=\"output\"><\/span><\/b> <\/div>\n<div id=\"words\"><input class=\"input_label_calc\" type=\"button\" id=\"button_calc\" onclick=\"solution()\" value=\"Show Solution\"><\/div>\n<div id=\"solution_div\"><span id=\"solution_words\"><\/span><\/div>\n<div id=\"words\"><input class=\"input_label_calc\" type=\"button\" id=\"button_calc\" onclick=\"gen()\" value=\"Generate New Question\"><\/div>\n<p><script><\/p>\n<p>var globalThing= {}; \/\/ Globally scoped object<\/p>\n<p>function check() {\t\n    if(globalThing.q_selected==\"between\") {\n        if(globalThing.sd_multiplier==1) {\n        var solution = 68;\n        }\n        if(globalThing.sd_multiplier==2) {\n        var solution = 95;\n        }\n        if(globalThing.sd_multiplier==3) {\n        var solution = 99.7;\n        }\n    } \/\/end between\n    if(globalThing.q_selected==\"less than\") {\n        if(globalThing.sd_multiplier==1) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 84;\n            } else {\n            var solution = 16;\n            }\n        }\n        if(globalThing.sd_multiplier==2) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 97.5;\n            } else {\n            var solution = 2.5;\n            }\n        }\n        if(globalThing.sd_multiplier==3) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 99.85;\n            } else {\n            var solution = 0.15;\n            }\n        }\n    } \/\/end less than\n    if(globalThing.q_selected==\"greater than\") {\n        if(globalThing.sd_multiplier==1) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 16;\n            } else {\n            var solution = 84;\n            }\n        }\n        if(globalThing.sd_multiplier==2) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 2.5;\n            } else {\n            var solution = 97.5;\n            }\n        }\n        if(globalThing.sd_multiplier==3) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 0.15;\n            } else {\n            var solution = 99.85;\n            }\n        }\n    } \/\/end greater than<\/p>\n<p>\/\/check if user-entered solution matches correct solution\nvar user_answer = document.getElementById('answer').value;\n    if (user_answer == solution) {\n    document.getElementById('output').innerHTML = \"Correct!\"\n    } else {\n    document.getElementById('output').innerHTML = \"Not quite yet...\"\n    }<\/p>\n<p>\/\/toggle answer showing\nvar result_display = document.getElementById(\"words_output\");\nresult_display.style.display = \"block\";\n} \/\/end massive check() function<\/p>\n<p>function solution() {\t\n    if(globalThing.q_selected==\"between\") {\n        if(globalThing.sd_multiplier==1) {\n        var solution = 68;\n        document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 68% of data values fall within one standard deviation of the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located one standard deviation below the mean and \" + globalThing.sd_above.toFixed(1) + \" is located one standard deviation above the mean.<\/p>\n<p>Thus, <b>68%<\/b> of plants are between \" + globalThing.sd_below.toFixed(1) + \" and \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n        }\n        if(globalThing.sd_multiplier==2) {\n        var solution = 95;\n        document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located two standard deviations below the mean and \" + globalThing.sd_above.toFixed(1) + \" is located two standard deviations above the mean.<\/p>\n<p>Thus, <b>95%<\/b> of plants are between \" + globalThing.sd_below.toFixed(1) + \" and \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n        }\n        if(globalThing.sd_multiplier==3) {\n        var solution = 99.7;\n        document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 99.7% of data values fall within three standard deviations of the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located three standard deviations below the mean and \" + globalThing.sd_above.toFixed(1) + \" is located three standard deviations above the mean.<\/p>\n<p>Thus, <b>99.7%<\/b> of plants are between \" + globalThing.sd_below.toFixed(1) + \" and \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n        }\n    } \/\/end between\n    if(globalThing.q_selected==\"less than\") {\n        if(globalThing.sd_multiplier==1) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 84;\n                    document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 68% of data values fall within one standard deviation of the mean. This means that 34% of values fall between the mean and one standard deviation above the mean.<\/p>\n<p>In this example, \" + globalThing.sd_above.toFixed(1) + \" is located one standard deviation above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 34% = <b>84%<\/b> of values fall below \" + globalThing.sd_above.toFixed(1) + \".<\/p>\n<p>Thus, <b>84%<\/b> of plants are less than \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n            } else {\n            var solution = 16;                              document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 68% of data values fall within one standard deviation of the mean. This means that 34% of values fall between the mean and one standard deviation below the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located one standard deviation below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 34% = 84% of values fall above \" + globalThing.sd_below.toFixed(1) + \". This means that 100% - 84% = <b>16%<\/b> of values fall below \" + globalThing.sd_below.toFixed(1) + \".<\/p>\n<p>Thus, <b>16%<\/b> of plants are less than \" + globalThing.sd_below.toFixed(1) + \" inches tall.\";\n            }\n        }\n        if(globalThing.sd_multiplier==2) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 97.5;                           \n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean. This means that 47.5% of values fall between the mean and two standard deviations above the mean.<\/p>\n<p>In this example, \" + globalThing.sd_above.toFixed(1) + \" is located two standard deviations above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 47.5% = <b>97.5%<\/b> of values fall below \" + globalThing.sd_above.toFixed(1) + \".<\/p>\n<p>Thus, <b>97.5%<\/b> of plants are less than \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n            } else {\n            var solution = 2.5;\n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean. This means that 47.5% of values fall between the mean and two standard deviations below the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located two standard deviations below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 47.5% = 97.5% of values fall above \" + globalThing.sd_below.toFixed(1) + \". This means that 100% - 97.5% = <b>2.5%<\/b> of values fall below \" + globalThing.sd_below.toFixed(1) + \".<\/p>\n<p>Thus, <b>2.5%<\/b> of plants are less than \" + globalThing.sd_below.toFixed(1) + \" inches tall.\";\n            }\n        }\n        if(globalThing.sd_multiplier==3) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 99.85;                        \n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 99.7% of data values fall within three standard deviations of the mean. This means that 49.85% of values fall between the mean and three standard deviations above the mean.<\/p>\n<p>In this example, \" + globalThing.sd_above.toFixed(1) + \" is located three standard deviations above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 49.85% = <b>99.85%<\/b> of values fall below \" + globalThing.sd_above.toFixed(1) + \".<\/p>\n<p>Thus, <b>99.85%<\/b> of plants are less than \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n            } else {\n            var solution = 0.15;                       \n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 99.7% of data values fall within three standard deviations of the mean. This means that 49.85% of values fall between the mean and three standard deviations below the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located three standard deviations below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 49.85% = 99.85% of values fall above \" + globalThing.sd_below.toFixed(1) + \". This means that 100% - 99.85% = <b>0.15%<\/b> of values fall below \" + globalThing.sd_below.toFixed(1) + \".<\/p>\n<p>Thus, <b>0.15%<\/b> of plants are less than \" + globalThing.sd_below.toFixed(1) + \" inches tall.\";\n            }\n        }\n    } \/\/end less than\n    if(globalThing.q_selected==\"greater than\") {\n        if(globalThing.sd_multiplier==1) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 16;\n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 68% of data values fall within one standard deviation of the mean. This means that 34% of values fall between the mean and one standard deviation above the mean.<\/p>\n<p>In this example, \" + globalThing.sd_above.toFixed(1) + \" is located one standard deviation above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 34% = <b>84%<\/b> of values fall below \" + globalThing.sd_above.toFixed(1) + \". This means that 100% - 84% = <b>16%<\/b> of values fall above \" + globalThing.sd_above.toFixed(1) + \".<\/p>\n<p>Thus, <b>16%<\/b> of plants are greater than \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n            } else {\n            var solution = 84;\n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 68% of data values fall within one standard deviation of the mean. This means that 34% of values fall between the mean and one standard deviation below the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located one standard deviation below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 34% = <b>84%<\/b> of values fall above \" + globalThing.sd_below.toFixed(1) + \".<\/p>\n<p>Thus, <b>84%<\/b> of plants are greater than \" + globalThing.sd_below.toFixed(1) + \" inches tall.\";\n            }\n        }\n        if(globalThing.sd_multiplier==2) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 2.5;\n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean. This means that 47.5% of values fall between the mean and two standard deviations above the mean.<\/p>\n<p>In this example, \" + globalThing.sd_above.toFixed(1) + \" is located two standard deviations above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 47.5% = <b>97.5%<\/b> of values fall below \" + globalThing.sd_above.toFixed(1) + \". This means that 100% - 97.5% = <b>2.5%<\/b> of values fall above \" + globalThing.sd_above.toFixed(1) + \".<\/p>\n<p>Thus, <b>2.5%<\/b> of plants are greater than \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n            } else {\n            var solution = 97.5;\n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 95% of data values fall within two standard deviations of the mean. This means that 47.5% of values fall between the mean and two standard deviations below the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located two standard deviations below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 47.5% = <b>97.5%<\/b> of values fall above \" + globalThing.sd_below.toFixed(1) + \".<\/p>\n<p>Thus, <b>97.5%<\/b> of plants are greater than \" + globalThing.sd_below.toFixed(1) + \" inches tall.\";\n            }\n        }\n        if(globalThing.sd_multiplier==3) {\n            if(globalThing.sd_selected==globalThing.sd_above) {\n            var solution = 0.15;\n          document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 99.7% of data values fall within three standard deviations of the mean. This means that 49.85% of values fall between the mean and three standard deviations above the mean.<\/p>\n<p>In this example, \" + globalThing.sd_above.toFixed(1) + \" is located three standard deviations above the mean. Since we know that 50% of data values fall below the mean in a normal distribution, a total of 50% + 49.85% = <b>99.85%<\/b> of values fall below \" + globalThing.sd_above.toFixed(1) + \". This means that 100% - 99.85% = <b>0.15%<\/b> of values fall above \" + globalThing.sd_above.toFixed(1) + \".<\/p>\n<p>Thus, <b>0.15%<\/b> of plants are greater than \" + globalThing.sd_above.toFixed(1) + \" inches tall.\";\n            } else {\n            var solution = 99.85;\n            document.getElementById('solution_words').innerHTML = \"The Empirical Rule states that for a given dataset with a normal distribution, 99.7% of data values fall within three standard deviations of the mean. This means that 49.85% of values fall between the mean and three standard deviation below the mean.<\/p>\n<p>In this example, \" + globalThing.sd_below.toFixed(1) + \" is located three standard deviations below the mean. Since we know that 50% of data values fall above the mean in a normal distribution, a total of 50% + 49.85% = <b>99.85%<\/b> of values fall above \" + globalThing.sd_below.toFixed(1) + \".<\/p>\n<p>Thus, <b>99.85%<\/b> of plants are greater than \" + globalThing.sd_below.toFixed(1) + \" inches tall.\";\n            }\n        }\n    } \/\/end greater than<\/p>\n<p>\/\/toggle hide\/show solution\n  var solution_div = document.getElementById(\"solution_div\");\n  solution_div.style.display = \"block\";\n} \/\/end massive solution() function<\/p>\n<p>function gen() {\t\nvar mean = Math.round(jStat.uniform.sample(20, 50)*10)\/10;\nvar sd = Math.round(jStat.uniform.sample(2, 6)*10)\/10;<\/p>\n<p>var sd_options = [1, 2, 3];\nglobalThing.sd_multiplier = sd_options[Math.floor(Math.random()*sd_options .length)];<\/p>\n<p>globalThing.sd_above = mean - (-globalThing.sd_multiplier*sd);\nglobalThing.sd_below = mean - (globalThing.sd_multiplier*sd);<\/p>\n<p>sd_above_below = [globalThing.sd_above, globalThing.sd_below];\nglobalThing.sd_selected = sd_above_below[Math.floor(Math.random()*sd_above_below.length)];<\/p>\n<p>var q_options = [\"between\", \"less than\", \"greater than\"];\nglobalThing.q_selected = q_options[Math.floor(Math.random()*q_options .length)];<\/p>\n<p>if (globalThing.q_selected == \"less than\") {\ndocument.getElementById('scenario').innerHTML = \"less than \" + globalThing.sd_selected.toFixed(1);\n} else if (globalThing.q_selected == \"greater than\") {\ndocument.getElementById('scenario').innerHTML = \"greater than \" + globalThing.sd_selected.toFixed(1);\n} else {\ndocument.getElementById('scenario').innerHTML = \"between \" + globalThing.sd_below.toFixed(1) + \" and \" + globalThing.sd_above.toFixed(1);\n}<\/p>\n<p>\/\/fill in mean and sd in initial question\ndocument.getElementById('mean').innerHTML = mean;\ndocument.getElementById('sd').innerHTML = sd;<\/p>\n<p>\/\/toggle answer & solution to hide and clear input field\nvar result_display = document.getElementById(\"words_output\");\nresult_display.style.display = \"none\";\nvar solution_div = document.getElementById(\"solution_div\");\nsolution_div.style.display = \"none\";\ndocument.getElementById('answer').value = \"\";\n} \/\/end massive gen() function<\/p>\n<p>\/\/generate initial question\ngen();\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A regra pr\u00e1tica , \u00e0s vezes chamada de regra 68-95-99,7, afirma que para um determinado conjunto de dados com distribui\u00e7\u00e3o normal: 68% dos valores dos dados est\u00e3o dentro de um desvio padr\u00e3o da m\u00e9dia. 95% dos valores dos dados est\u00e3o dentro de dois desvios padr\u00e3o da m\u00e9dia. 99,7% dos valores dos dados est\u00e3o dentro de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-448","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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