{"id":1040,"date":"2023-06-22T01:45:16","date_gmt":"2023-06-22T01:45:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/binomial-distribution-dig-deeper\/"},"modified":"2025-05-17T03:07:15","modified_gmt":"2025-05-17T03:07:15","slug":"binomial-distribution-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/binomial-distribution-dig-deeper\/","title":{"raw":"Binomial Distribution: Fresh Take","rendered":"Binomial Distribution: Fresh Take"},"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;Determine if a probability model meets the conditions for a binomial 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;}\">Determine if a probability model meets the conditions for a binomial distribution<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use a binomial distribution to calculate probability&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 a binomial distribution to calculate probability<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Acceptance Sampling<\/h3>\r\n<p>So far, we explore the binomial distribution in the context of acceptance sampling.<\/p>\r\n<p><strong>Acceptance sampling<\/strong> is a method used heavily in quality control. Lots (or batches) of a product are sampled, and each item in the sample is determined to be \u201cconforming\u201d or \u201cnonconforming\u201d to a set of standards. If the number of nonconforming items is above a certain threshold (called the acceptable quality level), the lot is rejected.<\/p>\r\n<p>This method was first utilized during World War II in order to test munitions.[footnote]National Institute of Standards and Technology (n.d.). What kinds of lot acceptance sampling plans (LASPs) are there? https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm[\/footnote] Sampling plans today are often more complex than this original model and may involve multi-stage sampling. There are quality control companies who work with organizations and businesses to apply statistical methods to a particular situation in order to determine what the proper sample size should be, as well as what the acceptable quality level of a sample should be.[footnote]American Society for Quality (n.d.). Attribute &amp; variable sampling plans and inspection procedures. https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling[\/footnote]<\/p>\r\n<p>Resources for learning about acceptance sampling:<\/p>\r\n<ul>\r\n\t<li><a href=\"https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK235721\/\">https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK235721\/<\/a> (discusses sampling plans for seafood safety determinations made by the FDA)<\/li>\r\n\t<li><a href=\"https:\/\/hbr.org\/1983\/09\/product-defects-and-productivity\">https:\/\/hbr.org\/1983\/09\/product-defects-and-productivity<\/a> (general discussion of these methods in <em>Harvard Business Review<\/em>)<\/li>\r\n\t<li><a href=\"https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm\">https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm<\/a> (description of acceptance sampling methods given by the National Institute of Standards and Technology, part of the U.S. Department of Commerce)<\/li>\r\n\t<li><a href=\"https:\/\/asq.org\/quality-resources\/history-of-quality\">https:\/\/asq.org\/quality-resources\/history-of-quality<\/a>, <a href=\"https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling\">https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling<\/a> (some information about the\u00a0history of acceptance sampling and its basics as part of the larger quality control discussion by the American Society for Quality)<\/li>\r\n<\/ul>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p><iframe title=\"Binomial distribution | Probability and Statistics | Khan Academy\" src=\"https:\/\/www.youtube.com\/embed\/WWv0RUxDfbs\" width=\"873\" height=\"491\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Determine if a probability model meets the conditions for a binomial 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;}\">Determine if a probability model meets the conditions for a binomial distribution<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use a binomial distribution to calculate probability&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 a binomial distribution to calculate probability<\/span><\/li>\n<\/ul>\n<\/section>\n<h3>Acceptance Sampling<\/h3>\n<p>So far, we explore the binomial distribution in the context of acceptance sampling.<\/p>\n<p><strong>Acceptance sampling<\/strong> is a method used heavily in quality control. Lots (or batches) of a product are sampled, and each item in the sample is determined to be \u201cconforming\u201d or \u201cnonconforming\u201d to a set of standards. If the number of nonconforming items is above a certain threshold (called the acceptable quality level), the lot is rejected.<\/p>\n<p>This method was first utilized during World War II in order to test munitions.<a class=\"footnote\" title=\"National Institute of Standards and Technology (n.d.). What kinds of lot acceptance sampling plans (LASPs) are there? https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm\" id=\"return-footnote-1040-1\" href=\"#footnote-1040-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Sampling plans today are often more complex than this original model and may involve multi-stage sampling. There are quality control companies who work with organizations and businesses to apply statistical methods to a particular situation in order to determine what the proper sample size should be, as well as what the acceptable quality level of a sample should be.<a class=\"footnote\" title=\"American Society for Quality (n.d.). Attribute &amp; variable sampling plans and inspection procedures. https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling\" id=\"return-footnote-1040-2\" href=\"#footnote-1040-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>Resources for learning about acceptance sampling:<\/p>\n<ul>\n<li><a href=\"https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK235721\/\">https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK235721\/<\/a> (discusses sampling plans for seafood safety determinations made by the FDA)<\/li>\n<li><a href=\"https:\/\/hbr.org\/1983\/09\/product-defects-and-productivity\">https:\/\/hbr.org\/1983\/09\/product-defects-and-productivity<\/a> (general discussion of these methods in <em>Harvard Business Review<\/em>)<\/li>\n<li><a href=\"https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm\">https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm<\/a> (description of acceptance sampling methods given by the National Institute of Standards and Technology, part of the U.S. Department of Commerce)<\/li>\n<li><a href=\"https:\/\/asq.org\/quality-resources\/history-of-quality\">https:\/\/asq.org\/quality-resources\/history-of-quality<\/a>, <a href=\"https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling\">https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling<\/a> (some information about the\u00a0history of acceptance sampling and its basics as part of the larger quality control discussion by the American Society for Quality)<\/li>\n<\/ul>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" title=\"Binomial distribution | Probability and Statistics | Khan Academy\" src=\"https:\/\/www.youtube.com\/embed\/WWv0RUxDfbs\" width=\"873\" height=\"491\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1040-1\">National Institute of Standards and Technology (n.d.). What kinds of lot acceptance sampling plans (LASPs) are there? https:\/\/www.itl.nist.gov\/div898\/handbook\/pmc\/section2\/pmc22.htm <a href=\"#return-footnote-1040-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1040-2\">American Society for Quality (n.d.). Attribute &amp; variable sampling plans and inspection procedures. https:\/\/asq.org\/quality-resources\/sampling\/attributes-variables-sampling <a href=\"#return-footnote-1040-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":19,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":2912,"module-header":"fresh_take","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\/1040"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1040\/revisions"}],"predecessor-version":[{"id":6944,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1040\/revisions\/6944"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/2912"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1040\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1040"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1040"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1040"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1040"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}