{"id":1037,"date":"2023-06-22T01:45:14","date_gmt":"2023-06-22T01:45:14","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/binomial-distribution-apply-it-1\/"},"modified":"2024-02-10T00:07:44","modified_gmt":"2024-02-10T00:07:44","slug":"binomial-distribution-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/binomial-distribution-apply-it-1\/","title":{"raw":"Binomial Distribution: Apply It 1","rendered":"Binomial Distribution: Apply It 1"},"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<h2>Acceptance Sampling and Binomial Distribution<\/h2>\r\n<p><img class=\"aligncenter wp-image-1540\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/10\/10175422\/Picture15.jpg\" alt=\"A construction worker looking at a machine in person and on the computer.\" width=\"645\" height=\"351\" \/><\/p>\r\n<p>Quality control, which often involves checking batches (called \u201clots\u201d) of products for defects, is a very important part of production. One method of quality control that became commonly used during World War II is called <strong>acceptance sampling.<\/strong>[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]<\/p>\r\n<p><strong>Acceptance Sampling<\/strong> is a quality control technique used to assess the quality of a product or a batch of products. It involves inspecting a random sample from the batch and deciding whether to accept or reject the entire batch based on the quality of the sampled items. Acceptance sampling is commonly used in manufacturing, especially when testing the entire batch would be time-consuming or costly. It is a practical and cost-effective way to ensure quality control, especially for large-scale production processes. It allows manufacturers to make decisions about the entire batch based on the evaluation of a smaller, manageable sample.<\/p>\r\n<p>In acceptance sampling, a random sample is drawn from each lot of a product, and the items in the sample are tested. Each item in the sample is designated as either \u201cconforming\u201d to a set of standards or \u201cnonconforming.\u201d If the number of nonconforming items is above a pre-determined threshold, then the whole lot of the product is rejected.<\/p>\r\n<p>Many industries today use multi-stage sampling plans if it is feasible, but we will focus on single-stage plans.[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<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]888[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]887[\/ohm2_question]<\/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<h2>Acceptance Sampling and Binomial Distribution<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1540\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5826\/2022\/10\/10175422\/Picture15.jpg\" alt=\"A construction worker looking at a machine in person and on the computer.\" width=\"645\" height=\"351\" \/><\/p>\n<p>Quality control, which often involves checking batches (called \u201clots\u201d) of products for defects, is a very important part of production. One method of quality control that became commonly used during World War II is called <strong>acceptance sampling.<\/strong><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-1037-1\" href=\"#footnote-1037-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p><strong>Acceptance Sampling<\/strong> is a quality control technique used to assess the quality of a product or a batch of products. It involves inspecting a random sample from the batch and deciding whether to accept or reject the entire batch based on the quality of the sampled items. Acceptance sampling is commonly used in manufacturing, especially when testing the entire batch would be time-consuming or costly. It is a practical and cost-effective way to ensure quality control, especially for large-scale production processes. It allows manufacturers to make decisions about the entire batch based on the evaluation of a smaller, manageable sample.<\/p>\n<p>In acceptance sampling, a random sample is drawn from each lot of a product, and the items in the sample are tested. Each item in the sample is designated as either \u201cconforming\u201d to a set of standards or \u201cnonconforming.\u201d If the number of nonconforming items is above a pre-determined threshold, then the whole lot of the product is rejected.<\/p>\n<p>Many industries today use multi-stage sampling plans if it is feasible, but we will focus on single-stage plans.<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-1037-2\" href=\"#footnote-1037-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm888\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=888&theme=lumen&iframe_resize_id=ohm888&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm887\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=887&theme=lumen&iframe_resize_id=ohm887&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1037-1\">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-1037-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1037-2\">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-1037-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":16,"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":"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\/1037"}],"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\/1037\/revisions"}],"predecessor-version":[{"id":5533,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1037\/revisions\/5533"}],"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\/1037\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1037"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1037"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1037"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}