{"id":1063,"date":"2023-06-22T01:45:30","date_gmt":"2023-06-22T01:45:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/connection-between-binomial-and-normal-distributions-learn-it-1\/"},"modified":"2023-10-23T13:07:22","modified_gmt":"2023-10-23T13:07:22","slug":"connection-between-binomial-and-normal-distributions-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/connection-between-binomial-and-normal-distributions-learn-it-1\/","title":{"raw":"Connection Between Binomial and Normal Distributions: Learn It 1","rendered":"Connection Between Binomial and Normal Distributions: Learn It 1"},"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<h2>Binomial Distribution<\/h2>\r\n<p>We defined a binomial experiment as an experiment consisting of a fixed number, [latex]n[\/latex], of independent Bernoulli trials that count the number of successes out of [latex]n[\/latex] trials. Notice that the number of successes in a binomial experiment is a discrete random variable. The distribution of this random variable is modeled with the binomial distribution.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>binomial mean and standard deviation<\/h3>\r\n<p>For a binomial experiment with a probability of success [latex]p[\/latex] on [latex]n[\/latex] trials, the mean [latex] \\mu[\/latex] and standard deviation [latex] \\sigma [\/latex] are defined as follows:<\/p>\r\n<ul>\r\n\t<li>The mean of the number of successes is [latex] \\mu = np[\/latex].<\/li>\r\n\t<li>The standard deviation of the number of successes is [latex] \\sigma = \\sqrt{np(1-p)} [\/latex].<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1541[\/ohm2_question]<\/section>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1545[\/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<h2>Binomial Distribution<\/h2>\n<p>We defined a binomial experiment as an experiment consisting of a fixed number, [latex]n[\/latex], of independent Bernoulli trials that count the number of successes out of [latex]n[\/latex] trials. Notice that the number of successes in a binomial experiment is a discrete random variable. The distribution of this random variable is modeled with the binomial distribution.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>binomial mean and standard deviation<\/h3>\n<p>For a binomial experiment with a probability of success [latex]p[\/latex] on [latex]n[\/latex] trials, the mean [latex]\\mu[\/latex] and standard deviation [latex]\\sigma[\/latex] are defined as follows:<\/p>\n<ul>\n<li>The mean of the number of successes is [latex]\\mu = np[\/latex].<\/li>\n<li>The standard deviation of the number of successes is [latex]\\sigma = \\sqrt{np(1-p)}[\/latex].<\/li>\n<\/ul>\n<\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1541\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1541&theme=lumen&iframe_resize_id=ohm1541&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1545\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1545&theme=lumen&iframe_resize_id=ohm1545&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":20,"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\/1063"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1063\/revisions"}],"predecessor-version":[{"id":4088,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1063\/revisions\/4088"}],"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\/1063\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1063"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1063"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}