{"id":1065,"date":"2023-06-22T01:45:31","date_gmt":"2023-06-22T01:45:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/connection-between-binomial-and-normal-distributions-learn-it-3\/"},"modified":"2023-11-09T19:28:03","modified_gmt":"2023-11-09T19:28:03","slug":"connection-between-binomial-and-normal-distributions-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/connection-between-binomial-and-normal-distributions-learn-it-3\/","title":{"raw":"Connection Between Binomial and Normal Distributions: Learn It 3","rendered":"Connection Between Binomial and Normal Distributions: Learn It 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Use normal probability distribution to calculate binomial probabilities<\/li>\r\n\t<li>Check the conditions for applying a normal distribution to approximate a binomial distribution<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Connection Between Binomial and Normal Distributions<\/h3>\r\n<p>Oftentimes, it is adequate to use the mean and standard deviation to describe the most likely values for the number of successes. For large [latex] n~(\\mbox{when}~np\\geq 10 \\mbox{ and } n(1 \u2013 p) \\geq 10) [\/latex], the binomial distribution has an approximate bell shape. So, we can use the normal distribution to approximate the binomial distribution and conclude that nearly all possibilities for the number of successes fall between the mean and [latex]\u00b13[\/latex] standard deviations.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1547[\/ohm2_question]<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/binomialdist\/ \" width=\"100%\" height=\"925\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/binomialdist\/\" 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]1023[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Use normal probability distribution to calculate binomial probabilities<\/li>\n<li>Check the conditions for applying a normal distribution to approximate a binomial distribution<\/li>\n<\/ul>\n<\/section>\n<h3>Connection Between Binomial and Normal Distributions<\/h3>\n<p>Oftentimes, it is adequate to use the mean and standard deviation to describe the most likely values for the number of successes. For large [latex]n~(\\mbox{when}~np\\geq 10 \\mbox{ and } n(1 \u2013 p) \\geq 10)[\/latex], the binomial distribution has an approximate bell shape. So, we can use the normal distribution to approximate the binomial distribution and conclude that nearly all possibilities for the number of successes fall between the mean and [latex]\u00b13[\/latex] standard deviations.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1547\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1547&theme=lumen&iframe_resize_id=ohm1547&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/binomialdist\/\" width=\"100%\" height=\"925\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/binomialdist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1023\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1023&theme=lumen&iframe_resize_id=ohm1023&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":2912,"module-header":"learn_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\/1065"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1065\/revisions"}],"predecessor-version":[{"id":4320,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1065\/revisions\/4320"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/2912"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1065\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1065"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1065"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1065"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}