{"id":193903,"date":"2025-02-21T06:08:50","date_gmt":"2025-02-21T06:08:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193903"},"modified":"2025-02-21T06:08:52","modified_gmt":"2025-02-21T06:08:52","slug":"it-has-been-estimated-that-about-30-of-frozen-chickens-contain-enough-salmonella-bacteria-to-cause-illness-if-imprperly-cooked","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/21\/it-has-been-estimated-that-about-30-of-frozen-chickens-contain-enough-salmonella-bacteria-to-cause-illness-if-imprperly-cooked\/","title":{"rendered":"it has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if imprperly cooked"},"content":{"rendered":"\n

it has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if imprperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens? A) .882 B) .961 C) .039 D) .079<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The correct answer is C) 0.039<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

This problem follows a binomial probability distribution<\/strong> since each frozen chicken can either be contaminated or not. The probability of contamination per chicken is 30% (0.30)<\/strong>, and the consumer purchases 12 chickens<\/strong>. We define:<\/p>\n\n\n\n

    \n
  • ( n = 12 ) (total chickens)<\/li>\n\n\n\n
  • ( p = 0.30 ) (probability of contamination per chicken)<\/li>\n\n\n\n
  • ( X ) is the number of contaminated chickens, which follows a binomial distribution:
    [
    X \\sim Binomial(n=12, p=0.30)
    ]<\/li>\n\n\n\n
  • We need to find ( P(X > 6) ), i.e., the probability that more than 6 chickens are contaminated<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Using the cumulative distribution function (CDF)<\/strong> of the binomial distribution, we compute:<\/p>\n\n\n\n

    [
    P(X > 6) = 1 – P(X \\leq 6)
    ]<\/p>\n\n\n\n

    Using statistical calculations, ( P(X \\leq 6) ) is approximately 0.9614<\/strong>, so:<\/p>\n\n\n\n

    [
    P(X > 6) = 1 – 0.9614 = 0.0386
    ]<\/p>\n\n\n\n

    Rounding to three decimal places gives 0.039<\/strong>, which matches option C<\/strong>.<\/p>\n\n\n\n

    Interpretation:<\/h3>\n\n\n\n

    This result tells us that there is only about a 3.9% chance<\/strong> that more than 6 out of 12 frozen chickens will be contaminated. While contamination is possible, having a majority of the chickens (more than half) contaminated is relatively unlikely.<\/p>\n\n\n\n

    Now, I’ll generate an image illustrating the binomial probability distribution for this scenario.<\/p>\n\n\n\n

    The bar chart above visualizes the binomial probability distribution<\/strong> for this problem. The red bars highlight the probability of having more than 6 contaminated chickens<\/strong> (i.e., ( P(X > 6) )). This confirms that the probability is small, around 0.039 (3.9%)<\/strong>.<\/p>\n\n\n\n

    Let me know if you need further clarification!<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    it has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if imprperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens? A) .882 B) .961 C) .039 D) .079 The Correct Answer and Explanation is : […]<\/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-193903","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193903","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=193903"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193903\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}