{"id":447,"date":"2023-07-29T21:10:12","date_gmt":"2023-07-29T21:10:12","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e5%ae%9f%e8%b7%b5%e7%9a%84%e3%81%aa%e3%83%ab%e3%83%bc%e3%83%ab%e3%81%ae%e7%b5%8c%e9%a8%93%e7%9a%84%e5%95%8f%e9%a1%8c\/"},"modified":"2023-07-29T21:10:12","modified_gmt":"2023-07-29T21:10:12","slug":"%e5%ae%9f%e8%b7%b5%e7%9a%84%e3%81%aa%e3%83%ab%e3%83%bc%e3%83%ab%e3%81%ae%e7%b5%8c%e9%a8%93%e7%9a%84%e5%95%8f%e9%a1%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e5%ae%9f%e8%b7%b5%e7%9a%84%e3%81%aa%e3%83%ab%e3%83%bc%e3%83%ab%e3%81%ae%e7%b5%8c%e9%a8%93%e7%9a%84%e5%95%8f%e9%a1%8c\/","title":{"rendered":"\u7d4c\u9a13\u5247\u3092\u5b9f\u8df5\u3059\u308b\u969b\u306e\u554f\u984c\u70b9"},"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\">68-95-99.7 \u30eb\u30fc\u30eb\u3068\u3082\u547c\u3070\u308c\u308b<b>\u7d4c\u9a13\u5247<\/b>\u3067\u306f\u3001\u6b63\u898f\u5206\u5e03\u3092\u6301\u3064\u7279\u5b9a\u306e\u30c7\u30fc\u30bf \u30bb\u30c3\u30c8\u306b\u3064\u3044\u3066\u6b21\u306e\u3088\u3046\u306b\u8ff0\u3079\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/div>\n<div id=\"words_intro\">\u30c7\u30fc\u30bf\u5024\u306e<b>68% \u306f<\/b>\u5e73\u5747\u5024\u306e 1 \u6a19\u6e96\u504f\u5dee\u4ee5\u5185\u306b\u3042\u308a\u307e\u3059\u3002<\/div>\n<div id=\"words_intro\">\u30c7\u30fc\u30bf\u5024\u306e<b>95% \u306f<\/b>\u5e73\u5747\u5024\u306e 2 \u6a19\u6e96\u504f\u5dee\u4ee5\u5185\u306b\u3042\u308a\u307e\u3059\u3002<\/div>\n<div id=\"words_intro\">\u30c7\u30fc\u30bf\u5024\u306e<b>99.7% \u304c<\/b>\u5e73\u5747\u5024\u306e 3 \u6a19\u6e96\u504f\u5dee\u4ee5\u5185\u306b\u53ce\u307e\u308a\u307e\u3059\u3002<\/div>\n<div id=\"words_intro\">\u4ee5\u4e0b\u306e\u7df4\u7fd2\u554f\u984c\u3092\u4f7f\u7528\u3057\u3066\u3001\u7d4c\u9a13\u5247\u306e\u77e5\u8b58\u3092\u30c6\u30b9\u30c8\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/div>\n<hr id=\"hr_top\">\n<div id=\"words_intro\">\u7279\u5b9a\u306e\u5ead\u306e\u690d\u7269\u306e\u9ad8\u3055\u306f\u3001\u5e73\u5747<span id=\"mean\">12.3<\/span>\u30a4\u30f3\u30c1\u3001\u6a19\u6e96\u504f\u5dee<span id=\"sd\">4.1<\/span>\u30a4\u30f3\u30c1\u3067\u901a\u5e38\u5206\u5e03\u3057\u307e\u3059\u3002<\/div>\n<div id=\"words_intro\"><b>\u7d4c\u9a13\u5247\u3092\u4f7f\u7528\u3057\u3066\u3001\u9ad8\u3055<span id=\"scenario\">8.2 \uff5e 16.4<\/span>\u30a4\u30f3\u30c1\u306e\u690d\u7269\u306e\u5272\u5408\u3092\u63a8\u5b9a\u3057\u307e\u3059\u3002<\/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. 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