{"id":231,"date":"2023-12-07T14:55:07","date_gmt":"2023-12-07T19:55:07","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=part&#038;p=231"},"modified":"2024-07-03T14:54:39","modified_gmt":"2024-07-03T18:54:39","slug":"continuous-probability-distributions","status":"publish","type":"part","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/part\/continuous-probability-distributions\/","title":{"raw":"Binomial Distributions","rendered":"Binomial Distributions"},"content":{"raw":"<h2>Binomial Probability Distributions<\/h2>\r\nIn this section, we examine Binomial Probability Distributions:\r\n\r\n[caption id=\"attachment_1682\" align=\"alignnone\" width=\"688\"]<a href=\"https:\/\/www.wolframalpha.com\/input?i=graph+binomial+distribution\"><img class=\"wp-image-1682 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs.jpg\" alt=\"Binomial Distribution Graphs for Different Values of p\" width=\"688\" height=\"238\" \/><\/a> Binomial distribution graphs for different values of p[\/caption]\r\n<ul>\r\n \t<li>They are discrete distributions<\/li>\r\n \t<li>They measure the probability of a certain number, [latex]x[\/latex], of successes occurring<\/li>\r\n \t<li>We need both the number of trials ([latex]n[\/latex]), and the probability of success ([latex]p[\/latex]) to define a binomial distribution<\/li>\r\n<\/ul>\r\n<h2>The sections are organized as follows:<\/h2>\r\n<ol>\r\n \t<li>An introduction, properties of Binomial Distributions and how to calculate the probability of exactly [latex]x[\/latex] successes using the formula.<\/li>\r\n \t<li>How to calculate the probability of exactly [latex]x[\/latex] successes using the Excel's =BINOM.DIST function.<\/li>\r\n \t<li>How to calculate the probability of at most [latex] x[\/latex] number of successes.<\/li>\r\n \t<li>How to calculate the probability of more than [latex] x[\/latex] number of successes.<\/li>\r\n \t<li>How to calculate the probability of at least [latex] x[\/latex] successes or, [latex]P(X \\ge x)[\/latex].<\/li>\r\n \t<li>How to calculate the mean and standard deviation of binomial distributions.<\/li>\r\n<\/ol>","rendered":"<h2>Binomial Probability Distributions<\/h2>\n<p>In this section, we examine Binomial Probability Distributions:<\/p>\n<figure id=\"attachment_1682\" aria-describedby=\"caption-attachment-1682\" style=\"width: 688px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.wolframalpha.com\/input?i=graph+binomial+distribution\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1682 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs.jpg\" alt=\"Binomial Distribution Graphs for Different Values of p\" width=\"688\" height=\"238\" srcset=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs.jpg 688w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs-300x104.jpg 300w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs-65x22.jpg 65w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs-225x78.jpg 225w, https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2023\/12\/Binomial_Graphs-350x121.jpg 350w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/a><figcaption id=\"caption-attachment-1682\" class=\"wp-caption-text\">Binomial distribution graphs for different values of p<\/figcaption><\/figure>\n<ul>\n<li>They are discrete distributions<\/li>\n<li>They measure the probability of a certain number, [latex]x[\/latex], of successes occurring<\/li>\n<li>We need both the number of trials ([latex]n[\/latex]), and the probability of success ([latex]p[\/latex]) to define a binomial distribution<\/li>\n<\/ul>\n<h2>The sections are organized as follows:<\/h2>\n<ol>\n<li>An introduction, properties of Binomial Distributions and how to calculate the probability of exactly [latex]x[\/latex] successes using the formula.<\/li>\n<li>How to calculate the probability of exactly [latex]x[\/latex] successes using the Excel&#8217;s =BINOM.DIST function.<\/li>\n<li>How to calculate the probability of at most [latex]x[\/latex] number of successes.<\/li>\n<li>How to calculate the probability of more than [latex]x[\/latex] number of successes.<\/li>\n<li>How to calculate the probability of at least [latex]x[\/latex] successes or, [latex]P(X \\ge x)[\/latex].<\/li>\n<li>How to calculate the mean and standard deviation of binomial distributions.<\/li>\n<\/ol>\n","protected":false},"parent":0,"menu_order":5,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-231","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/231","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/231\/revisions"}],"predecessor-version":[{"id":2502,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/231\/revisions\/2502"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=231"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=231"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=231"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}