{"id":1760,"date":"2021-09-07T19:14:28","date_gmt":"2021-09-07T19:14:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1760"},"modified":"2023-12-05T09:20:21","modified_gmt":"2023-12-05T09:20:21","slug":"summary-using-the-normal-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-using-the-normal-distribution\/","title":{"raw":"Summary: Using the Normal Distribution","rendered":"Summary: Using the Normal Distribution"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Normal distribution tables and technology can be used to calculate probabilities of find percentiles associated with the normal distribution.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">To use a normal distribution table, values need to be converted to <em>z<\/em>-scores.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A cutoff associated with a certain percentile is referred to as a critical value.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>inverse function: <\/strong>a function where the input of the original function becomes the output of the inverse function\u200b\u200b\r\n\r\n<strong>normal distribution:<\/strong> a continuous random variable (RV) with pdf [latex]f(x)=\\frac{1}{\\sigma \\sqrt{2 \\pi}} e \\frac{-(x-M)^{2}}{2 \\sigma ^{2}}[\/latex]\u00a0where <em>\u03bc<\/em> is the mean of the distribution and <em>\u03c3<\/em> is the standard deviation; notation: X ~ N(\u03bc, \u03c3). If <em>\u03bc<\/em> = 0 and <em>\u03c3<\/em> = 1, the RV is called the standard normal distribution.","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Normal distribution tables and technology can be used to calculate probabilities of find percentiles associated with the normal distribution.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">To use a normal distribution table, values need to be converted to <em>z<\/em>-scores.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A cutoff associated with a certain percentile is referred to as a critical value.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>inverse function: <\/strong>a function where the input of the original function becomes the output of the inverse function\u200b\u200b<\/p>\n<p><strong>normal distribution:<\/strong> a continuous random variable (RV) with pdf [latex]f(x)=\\frac{1}{\\sigma \\sqrt{2 \\pi}} e \\frac{-(x-M)^{2}}{2 \\sigma ^{2}}[\/latex]\u00a0where <em>\u03bc<\/em> is the mean of the distribution and <em>\u03c3<\/em> is the standard deviation; notation: X ~ N(\u03bc, \u03c3). If <em>\u03bc<\/em> = 0 and <em>\u03c3<\/em> = 1, the RV is called the standard normal distribution.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1760\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/6-key-terms\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/6-key-terms<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/6-key-terms\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1760","chapter","type-chapter","status-publish","hentry"],"part":256,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1760","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1760\/revisions"}],"predecessor-version":[{"id":3675,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1760\/revisions\/3675"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/256"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1760\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1760"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1760"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1760"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}