{"id":1272,"date":"2023-06-22T02:13:06","date_gmt":"2023-06-22T02:13:06","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-distribution-of-a-sample-mean-background-youll-need-2\/"},"modified":"2024-02-07T18:22:21","modified_gmt":"2024-02-07T18:22:21","slug":"sampling-distribution-of-a-sample-mean-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-distribution-of-a-sample-mean-background-youll-need-2\/","title":{"raw":"Module 11: Background You'll Need 2","rendered":"Module 11: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate probabilities using a normal distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate probabilities using a normal distribution.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>In statistics, we are often interested in finding probabilities involving a normal distribution. These probabilities are calculated by finding the area under a normal curve.<\/p>\r\n<p><img class=\"aligncenter wp-image-6933 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/19182559\/NormalDist-1.png\" alt=\"Sample normal distribution curve with a mean of 0 and a standard deviation of 1.\" width=\"650\" height=\"400\" \/><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1498[\/ohm2_question]<\/section>\r\n<section class=\"textbox recall\">The Empirical Rule states that, in a bell-shaped, unimodal distribution, almost all the observed data values lie within three standard deviations to either side of the mean. Specifically, [latex]68\\%[\/latex] of the observations lie within one standard deviation of the mean, [latex]95\\%[\/latex] of the observations lie within two standard deviations of the mean, and [latex]99.7\\%[\/latex] of the observations lie within three standard deviations of the mean. For this reason, the Empirical Rule is sometimes called the [latex]68-95-99.7[\/latex] rule.<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1523[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate probabilities using a normal distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate probabilities using a normal distribution.<\/span><\/li>\n<\/ul>\n<\/section>\n<p>In statistics, we are often interested in finding probabilities involving a normal distribution. These probabilities are calculated by finding the area under a normal curve.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-6933 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/19182559\/NormalDist-1.png\" alt=\"Sample normal distribution curve with a mean of 0 and a standard deviation of 1.\" width=\"650\" height=\"400\" \/><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1498\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1498&theme=lumen&iframe_resize_id=ohm1498&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox recall\">The Empirical Rule states that, in a bell-shaped, unimodal distribution, almost all the observed data values lie within three standard deviations to either side of the mean. Specifically, [latex]68\\%[\/latex] of the observations lie within one standard deviation of the mean, [latex]95\\%[\/latex] of the observations lie within two standard deviations of the mean, and [latex]99.7\\%[\/latex] of the observations lie within three standard deviations of the mean. For this reason, the Empirical Rule is sometimes called the [latex]68-95-99.7[\/latex] rule.<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1523\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1523&theme=lumen&iframe_resize_id=ohm1523&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1268,"module-header":"background_you_need","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\/1272"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1272\/revisions"}],"predecessor-version":[{"id":5451,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1272\/revisions\/5451"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1268"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1272\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1272"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1272"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1272"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}