{"id":1515,"date":"2024-05-10T20:19:58","date_gmt":"2024-05-11T00:19:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=1515"},"modified":"2024-05-10T20:50:20","modified_gmt":"2024-05-11T00:50:20","slug":"the-mean-and-standard-deviation-of-binomial-distributions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/the-mean-and-standard-deviation-of-binomial-distributions\/","title":{"raw":"The Mean and Standard Deviation of Binomial Distributions","rendered":"The Mean and Standard Deviation of Binomial Distributions"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate the mean and standard deviation of binomial distributions.\r\n\r\n<\/div>\r\n<\/div>\r\n<h2>Calculating the Mean<\/h2>\r\n<ul>\r\n \t<li>We can easily calculate the mean of a binomial distribution:<\/li>\r\n \t<li>[latex]\\mu = n \\times p [\/latex]<\/li>\r\n<\/ul>\r\n<h2>Calculating the Standard Deviation<\/h2>\r\n<ul>\r\n \t<li>We can also easily calculate the standard deviation of a binomial distribution:<\/li>\r\n \t<li>[latex]\\sigma = \\sqrt{n \\times p \\times (1-p)} [\/latex]<\/li>\r\n<\/ul>\r\n<h2>Example 29.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: Let us revisit the hotel example where we randomly sample 12 guests and the probability of any guest being from Canada is 65%. of the distribution.\r\n\r\n<span style=\"color: #003366\"><strong>Question<\/strong><\/span>: What are the mean and standard deviation for this problem?\r\n\r\n<span style=\"color: #003366\"><strong>Solution<\/strong><\/span>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example29-1.xlsx\">Click here<\/a> to download the Excel solution. Also, see the solutions below:\r\n<ul>\r\n \t<li>[latex]\\mu = n \\times p = 12 \\times 0.65 = 7.8 [\/latex]<\/li>\r\n \t<li>[latex]\\sigma = \\sqrt{n \\times p \\times (1-p)} = \\sqrt{12 \\times 0.65 \\times (1-0.65)} = 1.6523 [\/latex]<\/li>\r\n<\/ul>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate the mean and standard deviation of binomial distributions.<\/p>\n<\/div>\n<\/div>\n<h2>Calculating the Mean<\/h2>\n<ul>\n<li>We can easily calculate the mean of a binomial distribution:<\/li>\n<li>[latex]\\mu = n \\times p[\/latex]<\/li>\n<\/ul>\n<h2>Calculating the Standard Deviation<\/h2>\n<ul>\n<li>We can also easily calculate the standard deviation of a binomial distribution:<\/li>\n<li>[latex]\\sigma = \\sqrt{n \\times p \\times (1-p)}[\/latex]<\/li>\n<\/ul>\n<h2>Example 29.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: Let us revisit the hotel example where we randomly sample 12 guests and the probability of any guest being from Canada is 65%. of the distribution.<\/p>\n<p><span style=\"color: #003366\"><strong>Question<\/strong><\/span>: What are the mean and standard deviation for this problem?<\/p>\n<p><span style=\"color: #003366\"><strong>Solution<\/strong><\/span>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example29-1.xlsx\">Click here<\/a> to download the Excel solution. Also, see the solutions below:<\/p>\n<ul>\n<li>[latex]\\mu = n \\times p = 12 \\times 0.65 = 7.8[\/latex]<\/li>\n<li>[latex]\\sigma = \\sqrt{n \\times p \\times (1-p)} = \\sqrt{12 \\times 0.65 \\times (1-0.65)} = 1.6523[\/latex]<\/li>\n<\/ul>\n","protected":false},"author":865,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1515","chapter","type-chapter","status-publish","hentry"],"part":231,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1515","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1515\/revisions"}],"predecessor-version":[{"id":1523,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1515\/revisions\/1523"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/231"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1515\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=1515"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1515"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=1515"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=1515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}