To determine the height required to be in the top 2.5% of third graders, we use the properties of the normal distribution and find the corresponding z-score.<\/p>\n\n\n\n
Step 1: Identify given values Mean (\u03bc) = 52 Standard deviation (\u03c3) = 1.6 Top 2.5% corresponds to the 97.5th percentile in a normal distribution.<\/p>\n\n\n\n
Step 2: Find the z-score From statistical tables, the z-score corresponding to the 97.5th percentile is approximately 1.96<\/strong>.<\/p>\n\n\n\n Step 3: Use the z-score formula<\/p>\n\n\n\n X=\u03bc+z\u03c3X = \\mu + z\\sigma<\/p>\n\n\n\n Substituting values,<\/p>\n\n\n\n X=52+(1.96\u00d71.6)X = 52 + (1.96 \\times 1.6)<\/p>\n\n\n\n X=52+3.136X = 52 + 3.136<\/p>\n\n\n\n X=55.1X = 55.1<\/p>\n\n\n\n Thus, a third grader must be at least 55.1<\/strong> to be in the top 2.5% of the group.<\/p>\n\n\n\n The normal distribution is a symmetric probability function that describes how values cluster around the mean. In this case, student heights follow a bell-shaped curve centered at 52. The standard deviation of 1.6 indicates how spread out the heights are. The larger the standard deviation, the wider the spread.<\/p>\n\n\n\n To find the cutoff height for the tallest 2.5%, we use the z-score, which measures how many standard deviations a value is from the mean. Using statistical tables, we determined that a z-score of 1.96 corresponds to the 97.5th percentile. Plugging into the formula, we found that students taller than 55.1 are among the tallest 2.5%. This statistical method ensures an accurate cutoff point based on probability theory.<\/p>\n\n\n\n The heights of a group of 400 third graders are normally distributed with a mean of 52 inches and a standard deviation of 1.6 inches. What height would a third grader need to be in order to be in the top 2.5% tallest third graders in this group? Give your answer to 1 decimal place. […]<\/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-237098","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237098","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=237098"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237098\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation<\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"