{"id":233458,"date":"2025-06-13T06:40:35","date_gmt":"2025-06-13T06:40:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233458"},"modified":"2025-06-13T06:40:37","modified_gmt":"2025-06-13T06:40:37","slug":"0-0-89-201-use-the-ti-84-calculator-to-find-the-area-of-the-shaded-region","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/0-0-89-201-use-the-ti-84-calculator-to-find-the-area-of-the-shaded-region\/","title":{"rendered":"0 0.89 201 Use the TI-84 calculator to find the area of the shaded region."},"content":{"rendered":"\n<p>0 0.89 201 Use the TI-84 calculator to find the area of the shaded region.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the <strong>area of the shaded region<\/strong> on a TI-84 calculator, based on the input \u201c0 0.89 201,\u201d we assume that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>lower bound<\/strong> of integration is 0<\/li>\n\n\n\n<li>The <strong>upper bound<\/strong> of integration is 0.89<\/li>\n\n\n\n<li>The <strong>function<\/strong> is the <strong>standard normal distribution<\/strong>, where 201 refers to the normal cumulative area (z = 0.89)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Correct Answer:<\/strong><\/h3>\n\n\n\n<p>Using the TI-84:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Press <strong>2nd<\/strong> then <strong>VARS<\/strong> to access the <strong>DISTR<\/strong> menu.<\/li>\n\n\n\n<li>Choose option <strong>2:normalcdf(<\/strong><\/li>\n\n\n\n<li>Enter the values: scssCopyEdit<code>normalcdf(0, 0.89, 0, 1)<\/code> This inputs:\n<ul class=\"wp-block-list\">\n<li>Lower bound = 0<\/li>\n\n\n\n<li>Upper bound = 0.89<\/li>\n\n\n\n<li>Mean = 0 (standard normal)<\/li>\n\n\n\n<li>Standard deviation = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Press <strong>ENTER<\/strong><\/li>\n<\/ol>\n\n\n\n<p>\ud83d\udccc <strong>Result:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopyEdit<code>normalcdf(0, 0.89, 0, 1) \u2248 0.3133\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer:<\/strong><\/h3>\n\n\n\n<p><strong>The area of the shaded region is approximately 0.3133<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 <strong>Textbook-Style Explanation <\/strong><\/h3>\n\n\n\n<p>In statistics and probability, the area under a normal curve represents the probability or proportion of values falling within a certain range. The <strong>standard normal distribution<\/strong> has a <strong>mean (\u03bc) of 0<\/strong> and a <strong>standard deviation (\u03c3) of 1<\/strong>. This question asks for the area under the standard normal curve from <strong>z = 0<\/strong> to <strong>z = 0.89<\/strong>.<\/p>\n\n\n\n<p>To calculate this on a TI-84 calculator, we use the <strong>normalcdf (cumulative distribution function)<\/strong>, which computes the area under the normal curve between two z-values. The syntax is:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">luaCopyEdit<code>normalcdf(lower bound, upper bound, \u03bc, \u03c3)\n<\/code><\/pre>\n\n\n\n<p>Since this is a standard normal curve, \u03bc = 0 and \u03c3 = 1. We input:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopyEdit<code>normalcdf(0, 0.89, 0, 1)\n<\/code><\/pre>\n\n\n\n<p>This command instructs the calculator to find the area from z = 0 to z = 0.89. Pressing ENTER returns approximately <strong>0.3133<\/strong>, meaning that about <strong>31.33%<\/strong> of the data falls between these two z-values.<\/p>\n\n\n\n<p>This shaded region often represents a probability or proportion in a real-world context. For example, if scores on a test are normally distributed, 31.33% of students scored between the mean and 0.89 standard deviations above the mean.<\/p>\n\n\n\n<p>Using graphing calculators like the TI-84 simplifies statistical analysis by providing accurate results without needing tables or complex formulas.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-244.jpeg\" alt=\"\" class=\"wp-image-233459\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>0 0.89 201 Use the TI-84 calculator to find the area of the shaded region. The Correct Answer and Explanation is: To find the area of the shaded region on a TI-84 calculator, based on the input \u201c0 0.89 201,\u201d we assume that: \u2705 Correct Answer: Using the TI-84: \ud83d\udccc Result: scssCopyEditnormalcdf(0, 0.89, 0, 1) [&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-233458","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233458","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=233458"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233458\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}