{"id":266874,"date":"2025-07-23T07:54:26","date_gmt":"2025-07-23T07:54:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266874"},"modified":"2025-07-23T07:54:28","modified_gmt":"2025-07-23T07:54:28","slug":"iq-scores-have-mean-of-100-and-a-standard-deviation-of-15-mary-has-an-iq-of-103","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/iq-scores-have-mean-of-100-and-a-standard-deviation-of-15-mary-has-an-iq-of-103\/","title":{"rendered":"IQ scores have mean of 100 and a standard deviation of 15. Mary has an IQ of 103."},"content":{"rendered":"\n

point) IQ scores have mean of 100 and a standard deviation of 15. Mary has an IQ of 103. What is the difference between Mary’s IQ and the mean? Answer: () Convert Mary’s IQ score to a z-score_ Answer:<\/p>\n\n\n\n

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

To answer your question, let’s break it down step by step.<\/p>\n\n\n\n

1. Difference Between Mary’s IQ and the Mean<\/strong><\/h3>\n\n\n\n

We are given the following information:<\/p>\n\n\n\n

    \n
  • The population mean IQ is 100.<\/li>\n\n\n\n
  • The standard deviation is 15.<\/li>\n\n\n\n
  • Mary’s IQ is 103.<\/li>\n<\/ul>\n\n\n\n

    The difference between Mary’s IQ and the mean can be calculated using this simple formula: Difference=Mary\u2019s IQ\u2212Mean IQ\\text{Difference} = \\text{Mary’s IQ} – \\text{Mean IQ}Difference=Mary\u2019s IQ\u2212Mean IQ<\/p>\n\n\n\n

    Substitute the given values: Difference=103\u2212100=3\\text{Difference} = 103 – 100 = 3Difference=103\u2212100=3<\/p>\n\n\n\n

    So, the difference between Mary’s IQ and the mean is 3<\/strong>.<\/p>\n\n\n\n

    2. Converting Mary’s IQ to a Z-Score<\/strong><\/h3>\n\n\n\n

    To convert Mary’s IQ to a z-score, we use the formula for the z-score: Z=X\u2212\u03bc\u03c3Z = \\frac{X – \\mu}{\\sigma}Z=\u03c3X\u2212\u03bc\u200b<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • XXX is the raw score (Mary’s IQ = 103),<\/li>\n\n\n\n
    • \u03bc\\mu\u03bc is the mean (100),<\/li>\n\n\n\n
    • \u03c3\\sigma\u03c3 is the standard deviation (15).<\/li>\n<\/ul>\n\n\n\n

      Substitute the given values: Z=103\u221210015=315=0.2Z = \\frac{103 – 100}{15} = \\frac{3}{15} = 0.2Z=15103\u2212100\u200b=153\u200b=0.2<\/p>\n\n\n\n

      So, Mary’s z-score is 0.2<\/strong>.<\/p>\n\n\n\n

      Explanation:<\/h3>\n\n\n\n
        \n
      • Difference between IQ and the mean<\/strong>: This simply tells you how much higher or lower a specific IQ score is compared to the average (mean). In this case, Mary’s IQ is 3 points above the mean.<\/li>\n\n\n\n
      • Z-Score<\/strong>: The z-score is a measure of how many standard deviations a particular score is from the mean. A z-score of 0.2 means Mary’s IQ is 0.2 standard deviations above the average IQ of the population. Z-scores are useful for comparing different data points from different distributions, as they standardize the values.<\/li>\n<\/ul>\n\n\n\n

        In summary:<\/p>\n\n\n\n

          \n
        • The difference between Mary’s IQ and the mean is 3<\/strong>.<\/li>\n\n\n\n
        • Mary’s z-score is 0.2<\/strong>.<\/li>\n<\/ul>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          point) IQ scores have mean of 100 and a standard deviation of 15. Mary has an IQ of 103. What is the difference between Mary’s IQ and the mean? Answer: () Convert Mary’s IQ score to a z-score_ Answer: The Correct Answer and Explanation is: To answer your question, let’s break it down step by […]<\/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-266874","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266874","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=266874"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266874\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}