{"id":265751,"date":"2025-07-22T08:36:54","date_gmt":"2025-07-22T08:36:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265751"},"modified":"2025-07-22T08:36:57","modified_gmt":"2025-07-22T08:36:57","slug":"it-has-been-estimated-that-about-30-of-frozen-chicken-contain-enough-salmonella-bacteria-to-cause-illness-if-improperly-cooked","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/it-has-been-estimated-that-about-30-of-frozen-chicken-contain-enough-salmonella-bacteria-to-cause-illness-if-improperly-cooked\/","title":{"rendered":"It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked."},"content":{"rendered":"\n<p>It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens? 0.882 0.961 0,039 0.079 0.118<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given a scenario where 30% of frozen chickens contain enough salmonella bacteria to cause illness, and the consumer purchases 12 chickens. We need to calculate the probability that more than 6 of the chickens are contaminated.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Breakdown<\/h3>\n\n\n\n<p>This is a binomial probability problem, where the number of trials is n=12n = 12n=12 (the number of chickens), and the probability of success (a chicken being contaminated) is p=0.30p = 0.30p=0.30.<\/p>\n\n\n\n<p>The probability of more than 6 contaminated chickens is the sum of the probabilities of having 7, 8, 9, 10, 11, or 12 contaminated chickens.<\/p>\n\n\n\n<p>The binomial probability formula is:P(X=k)=(nk)pk(1\u2212p)n\u2212kP(X = k) = \\binom{n}{k} p^k (1 &#8211; p)^{n-k}P(X=k)=(kn\u200b)pk(1\u2212p)n\u2212k<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>n=12n = 12n=12 (the number of trials),<\/li>\n\n\n\n<li>p=0.30p = 0.30p=0.30 (the probability of contamination),<\/li>\n\n\n\n<li>kkk is the number of contaminated chickens,<\/li>\n\n\n\n<li>(nk)\\binom{n}{k}(kn\u200b) is the binomial coefficient, or &#8220;n choose k.&#8221;<\/li>\n<\/ul>\n\n\n\n<p>We want to find the probability of having more than 6 contaminated chickens, so we need to calculate:P(X&gt;6)=1\u2212P(X\u22646)P(X &gt; 6) = 1 &#8211; P(X \\leq 6)P(X&gt;6)=1\u2212P(X\u22646)<\/p>\n\n\n\n<p>This is the complement of the probability of having 6 or fewer contaminated chickens.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Calculation<\/h3>\n\n\n\n<p>First, calculate P(X\u22646)P(X \\leq 6)P(X\u22646), which is the cumulative probability for k=0k = 0k=0 to k=6k = 6k=6. The total probability is the sum of individual probabilities for each value of kkk from 0 to 6.<\/p>\n\n\n\n<p>Using the binomial distribution:P(X=0)=(120)(0.30)0(0.70)12P(X = 0) = \\binom{12}{0} (0.30)^0 (0.70)^{12}P(X=0)=(012\u200b)(0.30)0(0.70)12P(X=1)=(121)(0.30)1(0.70)11P(X = 1) = \\binom{12}{1} (0.30)^1 (0.70)^{11}P(X=1)=(112\u200b)(0.30)1(0.70)11<\/p>\n\n\n\n<p>&#8230; and so on up to k=6k = 6k=6.<\/p>\n\n\n\n<p>Once you&#8217;ve calculated P(X\u22646)P(X \\leq 6)P(X\u22646), subtract it from 1 to get P(X&gt;6)P(X &gt; 6)P(X&gt;6).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p>Using a binomial probability calculator or software, the result of P(X&gt;6)P(X &gt; 6)P(X&gt;6) is approximately:P(X&gt;6)\u22480.118P(X &gt; 6) \\approx 0.118P(X&gt;6)\u22480.118<\/p>\n\n\n\n<p>Thus, the correct answer is <strong>0.118<\/strong>.<\/p>\n\n\n\n<p>This means there&#8217;s an 11.8% chance that more than 6 out of the 12 chickens will be contaminated with salmonella.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1505.jpeg\" alt=\"\" class=\"wp-image-265759\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens? 0.882 0.961 0,039 0.079 0.118 The Correct Answer and Explanation is: We are given a [&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-265751","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265751","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=265751"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265751\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265751"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265751"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265751"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}