{"id":253,"date":"2023-01-18T17:03:32","date_gmt":"2023-01-18T22:03:32","guid":{"rendered":"https:\/\/opentextbc.ca\/busstatsancillary\/?post_type=chapter&#038;p=253"},"modified":"2023-01-18T18:19:50","modified_gmt":"2023-01-18T23:19:50","slug":"the-standard-normal-distribution","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/busstatsancillary\/chapter\/the-standard-normal-distribution\/","title":{"raw":"6.1 The Standard Normal Distribution","rendered":"6.1 The Standard Normal Distribution"},"content":{"raw":"The following activities and questions relate to material covered in <a href=\"https:\/\/openstax.org\/books\/introductory-business-statistics\/pages\/6-1-the-standard-normal-distribution\">Chapter 6.1 The Standard Normal Distribution<\/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 Rent Survey in October 2020 showed that the average unit rent was $1315, per month. Assuming the rental standard deviation \u03c3 = $ 150. The rental price is normally distributed. X ~ N (1315, 150). [footnote]Data source: Yukon Bureau of Statistics. (October, 2020). <em>Yukon rent survey October 2020<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/rent_oct20.pdf.[\/footnote] Calculate the z-score for a rental price of $1000 and interpret it using a complete sentence.<\/li>\r\n<\/ol>\r\n<h1>Solutions<\/h1>\r\n<ol>\r\n \t<li>[latex]Z=\\dfrac{X-\\mu}{\\sigma}&gt;\\dfrac{1000-1315}{150}=-2.1[\/latex]\r\nThe rental price of $1000 is 2.1 standard deviations below the mean of $1315, per month.<\/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\/6-1-the-standard-normal-distribution\">Chapter 6.1 The Standard Normal Distribution<\/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 Rent Survey in October 2020 showed that the average unit rent was $1315, per month. Assuming the rental standard deviation \u03c3 = $ 150. The rental price is normally distributed. X ~ N (1315, 150). <a class=\"footnote\" title=\"Data source: Yukon Bureau of Statistics. (October, 2020). Yukon rent survey October 2020. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/rent_oct20.pdf.\" id=\"return-footnote-253-1\" href=\"#footnote-253-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Calculate the z-score for a rental price of $1000 and interpret it using a complete sentence.<\/li>\n<\/ol>\n<h1>Solutions<\/h1>\n<ol>\n<li>[latex]Z=\\dfrac{X-\\mu}{\\sigma}>\\dfrac{1000-1315}{150}=-2.1[\/latex]<br \/>\nThe rental price of $1000 is 2.1 standard deviations below the mean of $1315, per month.<\/li>\n<\/ol>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-253-1\">Data source: Yukon Bureau of Statistics. (October, 2020). <em>Yukon rent survey October 2020<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/rent_oct20.pdf. <a href=\"#return-footnote-253-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","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-253","chapter","type-chapter","status-publish","hentry"],"part":81,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/253","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":5,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/253\/revisions"}],"predecessor-version":[{"id":258,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/253\/revisions\/258"}],"part":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/parts\/81"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/253\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/media?parent=253"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapter-type?post=253"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/contributor?post=253"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/license?post=253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}