{"id":162449,"date":"2024-11-06T18:41:13","date_gmt":"2024-11-06T18:41:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=162449"},"modified":"2024-11-06T18:41:15","modified_gmt":"2024-11-06T18:41:15","slug":"a-company-manufacturers-video-games-with-a-current-defect-rate-of-0-95","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/06\/a-company-manufacturers-video-games-with-a-current-defect-rate-of-0-95\/","title":{"rendered":"A company manufacturers video games with a current defect rate of 0.95%."},"content":{"rendered":"\n<p>A company manufacturers video games with a current defect rate of 0.95%. To make sure as few defective video games are delivered as possible, they are tested before delivery. The test is 98% accurate at determining if a video game is defective. If 100,000 products are manufactured and delivered in a month, Approximately how many defective products are expected to be delivered.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine how many defective products are expected to be delivered by the company, we can approach the problem step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given Information:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Defect rate<\/strong> = 0.95% (which means 0.0095 of the products are defective).<\/li>\n\n\n\n<li><strong>Test accuracy<\/strong> = 98% (the test correctly identifies defective products 98% of the time).<\/li>\n\n\n\n<li><strong>Total products manufactured and delivered<\/strong> = 100,000.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the total number of defective products.<\/h3>\n\n\n\n<p>The defect rate tells us the proportion of products that are defective. Thus, the expected number of defective products is:<br>[<br>\\text{Defective Products} = 100,000 \\times 0.0095 = 950<br>]<br>So, the company manufactures 950 defective products.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine how many defective products pass the test.<\/h3>\n\n\n\n<p>Since the test is 98% accurate, it correctly identifies 98% of the defective products. Therefore, the number of defective products that are correctly identified by the test is:<br>[<br>\\text{Correctly Identified Defective Products} = 950 \\times 0.98 = 931<br>]<br>Thus, 931 defective products are correctly identified as defective and are likely to be rejected.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Determine how many defective products pass the test.<\/h3>\n\n\n\n<p>The remaining 2% of defective products will be misidentified as non-defective. This is:<br>[<br>\\text{Missed Defective Products} = 950 \\times 0.02 = 19<br>]<br>So, 19 defective products will pass the test and be delivered to customers as non-defective.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Determine the number of non-defective products that are incorrectly identified as defective.<\/h3>\n\n\n\n<p>Since the test is 98% accurate, it correctly identifies 98% of non-defective products as non-defective. Therefore, 2% of non-defective products will be incorrectly identified as defective. The total number of non-defective products is:<br>[<br>\\text{Non-defective Products} = 100,000 &#8211; 950 = 99,050<br>]<br>The number of non-defective products misidentified as defective is:<br>[<br>\\text{Misidentified Non-defective Products} = 99,050 \\times 0.02 = 1,981<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Determine the total number of defective products delivered.<\/h3>\n\n\n\n<p>To find the total number of defective products that are delivered, we add the 19 defective products that passed the test (from Step 3) to the 1,981 non-defective products that were misidentified as defective (from Step 4):<br>[<br>\\text{Total Defective Products Delivered} = 19 + 1,981 = 2,000<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Approximately <strong>2,000 defective products<\/strong> are expected to be delivered to customers.<\/p>\n\n\n\n<p>This includes the 19 defective products that pass the test and are delivered as non-defective, along with the 1,981 non-defective products that are incorrectly flagged as defective. This highlights the importance of test accuracy and the resulting impact on product delivery quality.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A company manufacturers video games with a current defect rate of 0.95%. To make sure as few defective video games are delivered as possible, they are tested before delivery. The test is 98% accurate at determining if a video game is defective. If 100,000 products are manufactured and delivered in a month, Approximately how many [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-162449","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162449","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=162449"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162449\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162449"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162449"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162449"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}