{"id":268575,"date":"2025-07-24T06:57:08","date_gmt":"2025-07-24T06:57:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=268575"},"modified":"2025-07-24T06:57:10","modified_gmt":"2025-07-24T06:57:10","slug":"a-successful-basketball-player-has-a-height-of-6-feet-9-inches-or-206-cm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/24\/a-successful-basketball-player-has-a-height-of-6-feet-9-inches-or-206-cm\/","title":{"rendered":"A successful basketball player has a height of 6 feet 9 inches, or 206 cm"},"content":{"rendered":"\n<p>A successful basketball player has a height of 6 feet 9 inches, or 206 cm. Based on statistics from a data set, his height converts to the z score of 4.45. How many standard deviations is his height above the mean? The player&#8217;s height is ? standard deviation(s) above the mean.<\/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>The z-score is a measure of how many standard deviations a particular value is from the mean. The formula to calculate the z-score is: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 data point (the player&#8217;s height in this case),<\/li>\n\n\n\n<li>\u03bc\\mu\u03bc is the mean height of the dataset,<\/li>\n\n\n\n<li>\u03c3\\sigma\u03c3 is the standard deviation.<\/li>\n<\/ul>\n\n\n\n<p>In this case, the z-score for the player&#8217;s height is given as 4.45, which means the player\u2019s height is 4.45 standard deviations above the mean. To clarify:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A z-score of 4.45 means the player&#8217;s height is 4.45 times the size of the standard deviation above the average height of players in the dataset.<\/li>\n\n\n\n<li>The z-score formula indicates that for each standard deviation, the player&#8217;s height deviates from the mean in a certain proportion.<\/li>\n<\/ul>\n\n\n\n<p>Since the z-score is positive (4.45), we know the player&#8217;s height is above the average height of the dataset.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A z-score represents the number of standard deviations a value is from the mean. A z-score of 4.45 indicates that the basketball player&#8217;s height is far above the average for the population or dataset in question.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In general, a z-score around 0 means the value is close to the average.<\/li>\n\n\n\n<li>A z-score greater than 2 (or smaller than -2) typically indicates that the value is quite unusual or rare relative to the dataset.<\/li>\n<\/ul>\n\n\n\n<p>For example, if the average height of players in this dataset were 180 cm, and the standard deviation were 5 cm, a z-score of 4.45 means the player&#8217;s height is 4.45\u00d75=22.254.45 \\times 5 = 22.254.45\u00d75=22.25 cm above the mean. Thus, the player\u2019s height is much taller than most players in the dataset.<\/p>\n\n\n\n<p>Thus, <strong>the player&#8217;s height is 4.45 standard deviations above the mean<\/strong>.<\/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-banner6-1790.jpeg\" alt=\"\" class=\"wp-image-268576\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A successful basketball player has a height of 6 feet 9 inches, or 206 cm. Based on statistics from a data set, his height converts to the z score of 4.45. How many standard deviations is his height above the mean? The player&#8217;s height is ? standard deviation(s) above the mean. The Correct Answer and [&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-268575","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268575","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=268575"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268575\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=268575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=268575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=268575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}