{"id":253392,"date":"2025-07-12T04:57:34","date_gmt":"2025-07-12T04:57:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253392"},"modified":"2025-07-12T04:57:36","modified_gmt":"2025-07-12T04:57:36","slug":"find-the-z-score-for-an-iq-test-score-of-142-when-the-mean-is-100-and-the-slandard-deviation-is-15-0-2-8-2-8-0-127-18-78","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/12\/find-the-z-score-for-an-iq-test-score-of-142-when-the-mean-is-100-and-the-slandard-deviation-is-15-0-2-8-2-8-0-127-18-78\/","title":{"rendered":"&#8216;Find the z-score for an IQ test score of 142 when the mean is 100 and the slandard deviation is 15 0 ~2.8 2.8 0 127 18.78&#8217;"},"content":{"rendered":"\n<p>&#8216;Find the z-score for an IQ test score of 142 when the mean is 100 and the slandard deviation is 15 0 ~2.8 2.8 0 127 18.78&#8217;<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the <strong>z-score<\/strong> for an IQ test score of 142 when the mean is 100 and the standard deviation is 15, we use the formula: z=x\u2212\u03bc\u03c3z = \\frac{x &#8211; \\mu}{\\sigma}z=\u03c3x\u2212\u03bc\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xxx is the individual score (142),<\/li>\n\n\n\n<li>\u03bc\\mu\u03bc is the mean of the distribution (100),<\/li>\n\n\n\n<li>\u03c3\\sigma\u03c3 is the standard deviation (15).<\/li>\n<\/ul>\n\n\n\n<p>Substituting the values: z=142\u221210015z = \\frac{142 &#8211; 100}{15}z=15142\u2212100\u200b z=4215z = \\frac{42}{15}z=1542\u200b z=2.8z = 2.8z=2.8<\/p>\n\n\n\n<p>So, the <strong>z-score<\/strong> for an IQ score of 142 is <strong>2.8<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A <strong>z-score<\/strong> is a measure that describes a value&#8217;s position relative to the mean of a group of values. Specifically, it tells you how many standard deviations the value is away from the mean. A <strong>positive z-score<\/strong> indicates that the value is above the mean, while a <strong>negative z-score<\/strong> would indicate that the value is below the mean.<\/p>\n\n\n\n<p>In this case:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>mean IQ<\/strong> score is 100, which is considered the average.<\/li>\n\n\n\n<li>The <strong>standard deviation<\/strong> of 15 tells us the average amount by which individual scores vary from the mean.<\/li>\n\n\n\n<li>A score of 142 is <strong>42 points higher<\/strong> than the mean (100), and when divided by the standard deviation (15), it gives us a z-score of 2.8.<\/li>\n<\/ul>\n\n\n\n<p>This means that an IQ score of 142 is <strong>2.8 standard deviations above the average IQ score<\/strong>. This is considered quite a high score, placing the individual well above the average population in terms of IQ performance.<\/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-banner9-132.jpeg\" alt=\"\" class=\"wp-image-253400\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>&#8216;Find the z-score for an IQ test score of 142 when the mean is 100 and the slandard deviation is 15 0 ~2.8 2.8 0 127 18.78&#8217; The Correct Answer and Explanation is: To find the z-score for an IQ test score of 142 when the mean is 100 and the standard deviation is 15, [&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-253392","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253392","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=253392"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253392\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253392"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253392"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253392"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}