{"id":265,"date":"2023-01-18T19:20:08","date_gmt":"2023-01-19T00:20:08","guid":{"rendered":"https:\/\/opentextbc.ca\/busstatsancillary\/?post_type=chapter&#038;p=265"},"modified":"2023-01-18T19:31:34","modified_gmt":"2023-01-19T00:31:34","slug":"7-3-the-central-limit-theorem-for-proportions","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/busstatsancillary\/chapter\/7-3-the-central-limit-theorem-for-proportions\/","title":{"raw":"7.3 The Central Limit Theorem for Proportions","rendered":"7.3 The Central Limit Theorem for Proportions"},"content":{"raw":"The following activities and questions relate to material covered in <a href=\"https:\/\/openstax.org\/books\/introductory-business-statistics\/pages\/7-3-the-central-limit-theorem-for-proportions\">Chapter 7.3 The Central Limit Theorem for Proportions<\/a>\u00a0in\u00a0<a href=\"https:\/\/openstax.org\/details\/books\/introductory-business-statistics\" target=\"_blank\" rel=\"noopener\"><em>Introductory Business Statistics (OpenStax)<\/em><\/a>.\r\n<h1>Questions<\/h1>\r\n<ol>\r\n \t<li>A Yukon-based farm usually butchers chicken in mid-July and mid-August. If a chicken weighs less than 6 pounds, the farmer will keep them. The farmer weighed and butchered 220 chickens last year. One in forty chickens was not fit to keep. What is the standard deviation of the mean of the sampling distribution of sample proportions?<\/li>\r\n<\/ol>\r\n<h1>Solutions<\/h1>\r\n<ol>\r\n \t<li>[latex]\\sigma=\\sqrt{\\dfrac{p(1-p)}{n}}=\\sqrt{\\dfrac{\\frac{1}{40}(1-\\frac{1}{40})}{220}}=0.0105[\/latex]\r\nThe standard deviation of the mean of the sampling distribution of sample proportions is 0.0105.<\/li>\r\n<\/ol>","rendered":"<p>The following activities and questions relate to material covered in <a href=\"https:\/\/openstax.org\/books\/introductory-business-statistics\/pages\/7-3-the-central-limit-theorem-for-proportions\">Chapter 7.3 The Central Limit Theorem for Proportions<\/a>\u00a0in\u00a0<a href=\"https:\/\/openstax.org\/details\/books\/introductory-business-statistics\" target=\"_blank\" rel=\"noopener\"><em>Introductory Business Statistics (OpenStax)<\/em><\/a>.<\/p>\n<h1>Questions<\/h1>\n<ol>\n<li>A Yukon-based farm usually butchers chicken in mid-July and mid-August. If a chicken weighs less than 6 pounds, the farmer will keep them. The farmer weighed and butchered 220 chickens last year. One in forty chickens was not fit to keep. What is the standard deviation of the mean of the sampling distribution of sample proportions?<\/li>\n<\/ol>\n<h1>Solutions<\/h1>\n<ol>\n<li>[latex]\\sigma=\\sqrt{\\dfrac{p(1-p)}{n}}=\\sqrt{\\dfrac{\\frac{1}{40}(1-\\frac{1}{40})}{220}}=0.0105[\/latex]<br \/>\nThe standard deviation of the mean of the sampling distribution of sample proportions is 0.0105.<\/li>\n<\/ol>\n","protected":false},"author":123,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-265","chapter","type-chapter","status-publish","hentry"],"part":90,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/265","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":3,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/265\/revisions"}],"predecessor-version":[{"id":268,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/265\/revisions\/268"}],"part":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/parts\/90"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/265\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/media?parent=265"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapter-type?post=265"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/contributor?post=265"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/license?post=265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}