{"id":190729,"date":"2025-02-13T07:41:06","date_gmt":"2025-02-13T07:41:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190729"},"modified":"2025-02-13T07:41:08","modified_gmt":"2025-02-13T07:41:08","slug":"a-successful-basketball-player-has-a-height-of-6-feet-5-inches","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/13\/a-successful-basketball-player-has-a-height-of-6-feet-5-inches\/","title":{"rendered":"A successful basketball player has a height of 6 feet 5 \u200binches"},"content":{"rendered":"\n<p>A successful basketball player has a height of 6 feet 5 \u200binches, or<\/p>\n\n\n\n<p>196 cm. Based on statistics from a data\u200b set, his height converts to the z score of 3.02. How many standard deviations is his height above the\u200b mean?<br>(Round to two decimal places as\u200b needed.)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The z-score of 3.02 directly tells us that the basketball player&#8217;s height is 3.02 standard deviations above the mean height. Thus, the direct answer to your question is 3.02 standard deviations.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A z-score is a numerical measurement that describes a value&#8217;s relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The formula to calculate a z-score is:<\/p>\n\n\n\n<p>[ Z = \\frac{(X &#8211; \\mu)}{\\sigma} ]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( Z ) is the z-score.<\/li>\n\n\n\n<li>( X ) is the value being measured (in this case, the basketball player\u2019s height).<\/li>\n\n\n\n<li>( \\mu ) is the mean of the values.<\/li>\n\n\n\n<li>( \\sigma ) is the standard deviation of the values.<\/li>\n<\/ul>\n\n\n\n<p>A z-score of 3.02 implies that the basketball player&#8217;s height is 3.02 standard deviations above the mean height of the population from which this data set is drawn. Here&#8217;s what this tells us in terms of statistics:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Standard Deviations and Distribution<\/strong>: Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, whereas a high standard deviation means that the values are spread out over a wider range.<\/li>\n\n\n\n<li><strong>Interpreting the Z-Score<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A z-score of 0 indicates that the data point&#8217;s score is identical to the mean score.<\/li>\n\n\n\n<li>A z-score of 1.0 indicates a value that is one standard deviation from the mean.<\/li>\n\n\n\n<li>This player\u2019s z-score of 3.02 indicates that his height is significantly above the average, lying far outside the typical range found in the general population.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Implications in a Real-World Context<\/strong>: In sports, especially in basketball, being taller can be a significant advantage, contributing to a player&#8217;s success. The fact that this player is over three standard deviations taller than the average person could be one of the factors contributing to his success in basketball.<\/li>\n\n\n\n<li><strong>Statistical Rarity<\/strong>: A z-score of 3.02 suggests a rarity in height, as it is far from the mean. In a normally distributed curve, about 99.7% of values lie within three standard deviations of the mean. This player is thus taller than the vast majority of the population, highlighting how unusual his height is.<\/li>\n<\/ol>\n\n\n\n<p>In summary, the z-score of 3.02 means the player&#8217;s height is quite exceptional in the context of the general population, and this exceptional stature likely provides advantages in the sport of basketball.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A successful basketball player has a height of 6 feet 5 \u200binches, or 196 cm. Based on statistics from a data\u200b set, his height converts to the z score of 3.02. How many standard deviations is his height above the\u200b mean?(Round to two decimal places as\u200b needed.) The Correct Answer and Explanation is : The [&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-190729","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190729","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=190729"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190729\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}