{"id":253050,"date":"2025-07-11T17:59:35","date_gmt":"2025-07-11T17:59:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253050"},"modified":"2025-07-11T17:59:36","modified_gmt":"2025-07-11T17:59:36","slug":"on-a-standardized-test-where-the-results-are-distributed-normally-elliete-scored-246","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/on-a-standardized-test-where-the-results-are-distributed-normally-elliete-scored-246\/","title":{"rendered":"On a standardized test where the results are distributed normally, Elliete scored 246"},"content":{"rendered":"\n

On a standardized test where the results are distributed normally, Elliete scored 246. If the mean score was 182 with a standard deviation of 36, then what is Elliete’s percentile rank rounded to the nearest whole percent?<\/p>\n\n\n\n

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

To determine Elliete’s percentile rank, we need to calculate her z-score<\/strong>, which measures how many standard deviations her score is away from the mean, and then use that to find the percentile rank.<\/p>\n\n\n\n

Step 1: Calculate the Z-score<\/h3>\n\n\n\n

The formula for the z-score is: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 Elliete’s score (246)<\/li>\n\n\n\n
  • \u03bc\\mu\u03bc is the mean (182)<\/li>\n\n\n\n
  • \u03c3\\sigma\u03c3 is the standard deviation (36)<\/li>\n<\/ul>\n\n\n\n

    Substituting the values:z=246\u221218236=6436\u22481.78z = \\frac{246 – 182}{36} = \\frac{64}{36} \\approx 1.78z=36246\u2212182\u200b=3664\u200b\u22481.78<\/p>\n\n\n\n

    So, Elliete\u2019s z-score<\/strong> is approximately 1.78<\/strong>.<\/p>\n\n\n\n

    Step 2: Find the percentile corresponding to the z-score<\/h3>\n\n\n\n

    A z-score of 1.78 indicates how far Elliete’s score is above the mean. To find the percentile, we refer to the standard normal distribution table<\/strong> (or use a calculator that provides the cumulative probability for a z-score).<\/p>\n\n\n\n

    A z-score of 1.78<\/strong> corresponds to a cumulative probability of approximately 0.9625<\/strong>. This means that Elliete scored higher than about 96.25%<\/strong> of the people who took the test.<\/p>\n\n\n\n

    Step 3: Round to the nearest whole percent<\/h3>\n\n\n\n

    The percentile rank is rounded to the nearest whole number:Percentile rank=96%\\text{Percentile rank} = 96\\%Percentile rank=96%<\/p>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    Elliete\u2019s percentile rank is 96%<\/strong>, meaning she scored higher than 96%<\/strong> of the people who took the test.<\/p>\n\n\n\n

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

    On a standardized test where the results are distributed normally, Elliete scored 246. If the mean score was 182 with a standard deviation of 36, then what is Elliete’s percentile rank rounded to the nearest whole percent? The Correct Answer and Explanation is: To determine Elliete’s percentile rank, we need to calculate her z-score, which […]<\/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-253050","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253050","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=253050"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253050\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}