{"id":3157,"date":"2021-06-11T12:46:34","date_gmt":"2021-06-11T07:16:34","guid":{"rendered":"https:\/\/www.codingbroz.com\/?p=3157"},"modified":"2021-06-20T19:58:37","modified_gmt":"2021-06-20T14:28:37","slug":"day-six-central-limit-theorem-iii-solution","status":"publish","type":"post","link":"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/","title":{"rendered":"Day 6: The Central Limit Theorem III | 10 Days Of Statistics | HackerRank Solution"},"content":{"rendered":"\n<p>Hello coders, today we are going to solve<strong> Day 6: The Central Limit Theorem III HackerRank Solution<\/strong> which is a Part of <strong>10 Days of Statistics<\/strong> Series.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1200\" height=\"677\" src=\"https:\/\/www.codingbroz.com\/wp-content\/uploads\/2021\/06\/day-6-the-central-limit-theorem-iii-solution-codingbroz.png\" alt=\"Day 6: The Central Limit Theorem III\" class=\"wp-image-3159\" srcset=\"https:\/\/www.codingbroz.com\/wp-content\/uploads\/2021\/06\/day-6-the-central-limit-theorem-iii-solution-codingbroz.png 1200w, https:\/\/www.codingbroz.com\/wp-content\/uploads\/2021\/06\/day-6-the-central-limit-theorem-iii-solution-codingbroz-768x433.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/figure>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_65 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<label for=\"ez-toc-cssicon-toggle-item-662c3ffd07498\" class=\"ez-toc-cssicon-toggle-label\"><label class=\"ez-toc-title\">Table of Contents<\/label>\n<span class=\"ez-toc-cssicon\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #0090ff;color:#0090ff\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #0090ff;color:#0090ff\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-662c3ffd07498\" checked \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/#Objective\" title=\"Objective\">Objective<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/#Task\" title=\"Task\">Task<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/#Input_format\" title=\"Input format\">Input format<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/#Output_Format\" title=\"Output Format\">Output Format<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/#Solution_%E2%80%93_The_Central_Limit_Theorem_III\" title=\"Solution &#8211; The Central Limit Theorem III\">Solution &#8211; The Central Limit Theorem III<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.codingbroz.com\/day-six-central-limit-theorem-iii-solution\/#C\" title=\"C++\">C++<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Objective\"><\/span><strong>Objective<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In this challenge, we practice solving problems based on the&nbsp;<em>Central Limit Theorem<\/em>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Task\"><\/span><strong>Task<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>You have a sample of&nbsp;<strong>100<\/strong>&nbsp;values from a population with mean&nbsp;<strong><em>u<\/em> = 500<\/strong>&nbsp;and with standard deviation&nbsp;<strong><em>o<\/em> = 80<\/strong>. Compute the interval that covers the middle<strong>&nbsp;95%<\/strong>&nbsp;of the distribution of the sample mean; in other words, compute&nbsp;<strong><em>A<\/em><\/strong>&nbsp;and&nbsp;<strong><em>B<\/em><\/strong>&nbsp;such that&nbsp;<strong><em>P<\/em>(<em>A<\/em> &lt; <em>x<\/em> &lt; <em>B<\/em>) = 0.95<\/strong>. Use the value of&nbsp;<strong><em>z<\/em> = 1.96<\/strong>. Note that&nbsp;&nbsp;is the&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Standard_score\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">z-score<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Input_format\"><\/span><strong>Input format<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>There are five lines of input (shown below):<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>100\n500\n80\n.95\n1.96<\/code><\/pre>\n\n\n\n<p>The first line contains the sample size. The second and third lines contain the respective mean (<strong><em>u<\/em><\/strong>) and standard deviation (<strong><em>o<\/em><\/strong>). The fourth line contains the distribution percentage we want to cover (as a decimal), and the fifth line contains the value of&nbsp;<strong><em>z<\/em><\/strong>.<\/p>\n\n\n\n<p>If you do not wish to read this information from stdin, you can hard-code it into your program.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Output_Format\"><\/span><strong>Output Format<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Print the following two lines of output, rounded to a scale of&nbsp;<strong>2<\/strong>&nbsp;decimal places (i.e.,&nbsp;<strong>1.23<\/strong>&nbsp;format):<\/p>\n\n\n\n<ol><li>On the first line, print the value of&nbsp;<strong><em>A<\/em><\/strong>.<\/li><li>On the second line, print the value of&nbsp;<strong><em>B<\/em><\/strong>.<\/li><\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solution_%E2%80%93_The_Central_Limit_Theorem_III\"><\/span><strong>Solution &#8211; The Central Limit Theorem III<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"C\"><\/span><strong>C++<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;cmath>\n#include &lt;cstdio>\n#include &lt;vector>\n#include &lt;iostream>\n#include &lt;algorithm>\nusing namespace std;\n\n\ndouble normal_dist(double m, double sd, double x)\n{   \n    double p = 0.5*(1 + erf((x-m)\/(sd*sqrt(2.0))));\n    return p ; \n}\n\nint main() {\n    \/* Enter your code here. Read input from STDIN. Print output to STDOUT *\/  \n    \n    double mean = 500;\n    double std = 80;\n    int n = 100;\n    double zScore = 1.96;\n    \n    double marginOfError = zScore * std\/sqrt(n);\n    \n    printf(\"%0.2f\\n%0.2f\", mean - marginOfError, mean + marginOfError);\n    \n    return 0;\n}<\/pre>\n\n\n\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-5246141430412355\"\n     data-ad-slot=\"8798433565\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n\n\n\n<p><strong>Disclaimer:<\/strong> The above Problem <strong>(<a href=\"https:\/\/www.hackerrank.com\/challenges\/s10-the-central-limit-theorem-3\/problem\" target=\"_blank\" rel=\"noreferrer noopener\">The Central Limit Theorem III<\/a>)<\/strong> is generated by <strong>Hacker Rank<\/strong> but the Solution is Provided by <strong>CodingBroz<\/strong>. This tutorial is only for <strong>Educational<\/strong> and <strong>Learning<\/strong> Purpose.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hello coders, today we are going to solve Day 6: The Central Limit Theorem III HackerRank Solution which is a Part of 10 Days of Statistics Series.<\/p>\n","protected":false},"author":1,"featured_media":3159,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[9,187],"tags":[189,80,18],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.codingbroz.com\/wp-content\/uploads\/2021\/06\/day-6-the-central-limit-theorem-iii-solution-codingbroz.png","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/posts\/3157"}],"collection":[{"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/comments?post=3157"}],"version-history":[{"count":3,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/posts\/3157\/revisions"}],"predecessor-version":[{"id":3448,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/posts\/3157\/revisions\/3448"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/media\/3159"}],"wp:attachment":[{"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/media?parent=3157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/categories?post=3157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.codingbroz.com\/wp-json\/wp\/v2\/tags?post=3157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}