{"id":211536,"date":"2025-05-04T09:38:54","date_gmt":"2025-05-04T09:38:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=211536"},"modified":"2025-05-04T09:38:57","modified_gmt":"2025-05-04T09:38:57","slug":"the-caffeine-content-of-8-ounce-cans-of-a-certain-cola-drink-is-approximately-normally-distributed-with-mean-33-milligrams","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/04\/the-caffeine-content-of-8-ounce-cans-of-a-certain-cola-drink-is-approximately-normally-distributed-with-mean-33-milligrams\/","title":{"rendered":"The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams"},"content":{"rendered":"\n

The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?<\/p>\n\n\n\n

A. 196<\/p>\n\n\n\n

B. 8%<\/p>\n\n\n\n

C. 12%<\/p>\n\n\n\n

D. 16%<\/p>\n\n\n\n

E. 99%<\/p>\n\n\n\n

Determine each of the following: a. 49 div 8. b. 49 mod 8. c. -105 mod 12<\/p>\n\n\n\n

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

Question 1: Normal Distribution and Z-Score Interpretation<\/strong><\/h3>\n\n\n\n

We are given:<\/p>\n\n\n\n

    \n
  • Mean (\u03bc) = 33 mg<\/li>\n\n\n\n
  • A sample value = 35 mg<\/li>\n\n\n\n
  • Z-score = 1.2<\/li>\n<\/ul>\n\n\n\n

    The Z-score represents how many standard deviations a value is from the mean. A Z-score of 1.2<\/strong> means the value (35 mg) is 1.2 standard deviations above the mean<\/strong>.<\/p>\n\n\n\n

    To determine the percentage of cans with more than 35 mg<\/strong>, we want the area to the right<\/strong> of Z = 1.2 on the standard normal distribution curve.<\/p>\n\n\n\n

    Using a Z-table<\/strong> or calculator:<\/p>\n\n\n\n

      \n
    • P(Z < 1.2) \u2248 0.8849<\/strong>, meaning 88.49%<\/strong> of values fall below<\/strong> 35 mg.<\/li>\n\n\n\n
    • Therefore, P(Z > 1.2) = 1 – 0.8849 = 0.1151<\/strong>, or approximately 11.51%<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Rounded to the nearest whole number, the correct answer is:<\/strong><\/p>\n\n\n\n

      \n

      C. 12%<\/strong><\/p>\n<\/blockquote>\n\n\n\n

      Question 2: Modulo and Integer Division<\/strong><\/h3>\n\n\n\n

      a. 49 \u00f7 8<\/strong> (Integer Division):<\/h4>\n\n\n\n

      We divide 49 by 8:<\/p>\n\n\n\n

        \n
      • 8 goes into 49 6 times<\/strong> (because 8 \u00d7 6 = 48, which is the largest multiple of 8 less than or equal to 49)<\/li>\n<\/ul>\n\n\n\n

        \u2705 Answer: 6<\/strong><\/p>\n\n\n\n

        b. 49 mod 8<\/strong>:<\/h4>\n\n\n\n

        This is the remainder<\/strong> when 49 is divided by 8.<\/p>\n\n\n\n

          \n
        • 49 \u00f7 8 = 6 remainder 1<\/strong><\/li>\n<\/ul>\n\n\n\n

          \u2705 Answer: 1<\/strong><\/p>\n\n\n\n

          c. -105 mod 12<\/strong>:<\/h4>\n\n\n\n

          Modulo with negative numbers follows this rule:<\/p>\n\n\n\n

          \n

          a mod b = the remainder r such that 0 \u2264 r < b, and a \u2261 r (mod b)<\/strong><\/p>\n<\/blockquote>\n\n\n\n

          First, divide -105 by 12:<\/p>\n\n\n\n

            \n
          • -105 \u00f7 12 = -9 (because 12 \u00d7 -9 = -108, the closest lower multiple)<\/li>\n\n\n\n
          • The difference: -105 – (-108) = 3<\/strong><\/li>\n<\/ul>\n\n\n\n

            \u2705 Answer: 3<\/strong><\/p>\n\n\n\n

            This means:<\/p>\n\n\n\n

              \n
            • a. 49 \u00f7 8 = 6<\/strong><\/li>\n\n\n\n
            • b. 49 mod 8 = 1<\/strong><\/li>\n\n\n\n
            • c. -105 mod 12 = 3<\/strong><\/li>\n<\/ul>\n\n\n\n

              Summary<\/h3>\n\n\n\n
                \n
              • The caffeine question involves reading the Z-score and finding the area under the normal curve. The answer is 12%<\/strong>, based on the percentage of data lying above a Z-score of 1.2.<\/li>\n\n\n\n
              • Integer division and modulo problems are straightforward applications of division with remainders, even for negative values (which must yield a non-negative remainder).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg? A. […]<\/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-211536","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211536","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=211536"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211536\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}