{"id":1053,"date":"2023-06-22T01:45:25","date_gmt":"2023-06-22T01:45:25","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/normal-distribution-apply-it-3\/"},"modified":"2024-03-14T19:10:23","modified_gmt":"2024-03-14T19:10:23","slug":"normal-distribution-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/normal-distribution-apply-it-3\/","title":{"raw":"Normal Distribution: Apply It 3","rendered":"Normal Distribution: Apply It 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li class=\"li1\">Understand the properties, characteristics, and importance of a normal distribution in statistical analysis.<\/li>\r\n\t<li class=\"li1\">Explain how changing the mean and standard deviation will change the characteristics of a normal curve.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p><img class=\"aligncenter wp-image-5848 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22014524\/first-and-second-cousins.jpg\" alt=\"A diagram of a family tree, starting a great grandparent. It then branches into grandparent and great aunt or uncle. From the grandparent box, it goes into parent and aunt or uncle. From parent it goes to you, and aunt or uncle it goes to 1st cousin. After great aunt or uncle, it goes to 1st cousin once removed. Following that is a second cousin.\" width=\"300\" height=\"200\" \/>[footnote]https:\/\/www.rd.com\/article\/second-cousin-once-removed\/[\/footnote]<\/p>\r\n<p>We can also inverse the problem. What if we are given the probability and are asked to find the corresponding value?<\/p>\r\n<section class=\"textbox interact\">Steps on how to find the corresponding value (percentile):\r\n\r\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Click on the <strong>Find Percentile\/Quartile<\/strong>\u00a0tab at the top.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>Type in the <strong>Mean [latex]\\mu[\/latex]<\/strong> and <strong>Standard Deviation [latex]\\sigma[\/latex]<\/strong>\u00a0given in the question.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Choose <strong>Lower Tail<\/strong> if we are looking for the bottom percent. Choose <strong>Upper Tail<\/strong>\u00a0if we are looking for the top percent.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Type in the <strong>Probability in lower tail\/upper tail in [latex]\\%[\/latex]<\/strong>\u00a0form.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 5: <\/strong>The corresponding value can be found in the [latex]x[\/latex]-axis of the graph of under <strong>Percentile<\/strong>\u00a0in the table.<\/p>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>&nbsp;<\/p>\r\n<p><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1513[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]901[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li class=\"li1\">Understand the properties, characteristics, and importance of a normal distribution in statistical analysis.<\/li>\n<li class=\"li1\">Explain how changing the mean and standard deviation will change the characteristics of a normal curve.<\/li>\n<\/ul>\n<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5848 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22014524\/first-and-second-cousins.jpg\" alt=\"A diagram of a family tree, starting a great grandparent. It then branches into grandparent and great aunt or uncle. From the grandparent box, it goes into parent and aunt or uncle. From parent it goes to you, and aunt or uncle it goes to 1st cousin. After great aunt or uncle, it goes to 1st cousin once removed. Following that is a second cousin.\" width=\"300\" height=\"200\" \/><a class=\"footnote\" title=\"https:\/\/www.rd.com\/article\/second-cousin-once-removed\/\" id=\"return-footnote-1053-1\" href=\"#footnote-1053-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>We can also inverse the problem. What if we are given the probability and are asked to find the corresponding value?<\/p>\n<section class=\"textbox interact\">Steps on how to find the corresponding value (percentile):<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Click on the <strong>Find Percentile\/Quartile<\/strong>\u00a0tab at the top.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>Type in the <strong>Mean [latex]\\mu[\/latex]<\/strong> and <strong>Standard Deviation [latex]\\sigma[\/latex]<\/strong>\u00a0given in the question.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Choose <strong>Lower Tail<\/strong> if we are looking for the bottom percent. Choose <strong>Upper Tail<\/strong>\u00a0if we are looking for the top percent.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Type in the <strong>Probability in lower tail\/upper tail in [latex]\\%[\/latex]<\/strong>\u00a0form.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 5: <\/strong>The corresponding value can be found in the [latex]x[\/latex]-axis of the graph of under <strong>Percentile<\/strong>\u00a0in the table.<\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1513\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1513&theme=lumen&iframe_resize_id=ohm1513&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm901\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=901&theme=lumen&iframe_resize_id=ohm901&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1053-1\">https:\/\/www.rd.com\/article\/second-cousin-once-removed\/ <a href=\"#return-footnote-1053-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":18,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":3053,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1053"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1053\/revisions"}],"predecessor-version":[{"id":5956,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1053\/revisions\/5956"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/3053"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1053\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1053"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1053"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1053"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}