{"id":1158,"date":"2023-06-22T01:56:57","date_gmt":"2023-06-22T01:56:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-variability-apply-it-3\/"},"modified":"2025-05-16T02:58:06","modified_gmt":"2025-05-16T02:58:06","slug":"sampling-variability-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-variability-apply-it-3\/","title":{"raw":"Sampling Variability: Apply It 3","rendered":"Sampling Variability: Apply It 3"},"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;Check the conditions for normal approximation of a sampling distribution of a sample proportion&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions for normal approximation of a sampling distribution of a sample proportion.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Use the normal distribution to calculate probabilities and percentiles from a sampling distribution.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Find the sample size needed for a sampling distribution to have a desired standard deviation.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>Probabilities of Sampling Distribution of a Sample Proportion<\/strong><\/h2>\r\n<p>If a normal model is a good fit for a sampling distribution, we can apply the empirical rule and use\u00a0[latex]z[\/latex]-scores to determine probabilities. We can also use the statistical tool below to help us find probabilities.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1596[\/ohm2_question]<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1597[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for normal approximation of a sampling distribution of a sample proportion&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the conditions for normal approximation of a sampling distribution of a sample proportion.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Use the normal distribution to calculate probabilities and percentiles from a sampling distribution.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal distribution to calculate probabilities and percentiles from a sampling distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Find the sample size needed for a sampling distribution to have a desired standard deviation.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2><strong>Probabilities of Sampling Distribution of a Sample Proportion<\/strong><\/h2>\n<p>If a normal model is a good fit for a sampling distribution, we can apply the empirical rule and use\u00a0[latex]z[\/latex]-scores to determine probabilities. We can also use the statistical tool below to help us find probabilities.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1596\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1596&theme=lumen&iframe_resize_id=ohm1596&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_prop\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1597\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1597&theme=lumen&iframe_resize_id=ohm1597&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":26,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1126,"module-header":"apply_it","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\/1158"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1158\/revisions"}],"predecessor-version":[{"id":6713,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1158\/revisions\/6713"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1126"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1158\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1158"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1158"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1158"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}