{"id":246573,"date":"2025-07-07T09:02:35","date_gmt":"2025-07-07T09:02:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246573"},"modified":"2025-07-07T09:02:37","modified_gmt":"2025-07-07T09:02:37","slug":"use-the-ti-84-calculator-to-find-the-z-scores-that-bound-the-middle-82-of-the-area-under-the-standard-normal-curve","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/use-the-ti-84-calculator-to-find-the-z-scores-that-bound-the-middle-82-of-the-area-under-the-standard-normal-curve\/","title":{"rendered":"Use the TI-84 calculator to find the Z-scores that bound the middle 82% of the area under the standard normal curve."},"content":{"rendered":"\n
Use the TI-84 calculator to find the Z-scores that bound the middle 82% of the area under the standard normal curve. Enter the answers in ascending order and round to two decimal places. The Z-scores for the given area are [insert correct values here] and [insert correct values here].<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To find the Z-scores that bound the middle 82% of the area under the standard normal curve using the TI-84 calculator, follow these steps:<\/p>\n\n\n\n
Steps to Calculate:<\/h3>\n\n\n\n\n
Press the 2nd<\/code> button<\/strong>, then the VARS<\/code> button to access the DISTR<\/code> menu (where probability distributions are listed).<\/li>\n\n\n\n
Scroll down and select invNorm(<\/code>. This function will allow you to find the Z-scores for a given probability.<\/li>\n\n\n\n
The syntax for the invNorm<\/code> function is: invNorm(area to the left, mean, standard deviation)<\/code>.\n
\n
In this case, the mean is 0 and the standard deviation is 1 (because we are dealing with the standard normal distribution).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
Middle 82% of the area<\/strong> means that 82% of the area is between the two Z-scores, and 18% is split equally on both sides of the middle. This means:\n
\n
The area to the left of the lower Z-score is 9% (half of 18%).<\/li>\n\n\n\n
The area to the right of the upper Z-score is also 9%.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
Thus, the area to the left of the lower Z-score is 0.09, and the area to the left of the upper Z-score is 0.91 (since the total area under the curve is 1, and 1 – 0.09 = 0.91).<\/p>\n\n\n\n
\n
First Z-score (lower bound)<\/strong>:\n
\n
For the lower Z-score, enter invNorm(0.09, 0, 1)<\/code> into the calculator.<\/li>\n\n\n\n
The result is approximately -1.34<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
Second Z-score (upper bound)<\/strong>:\n
\n
For the upper Z-score, enter invNorm(0.91, 0, 1)<\/code> into the calculator.<\/li>\n\n\n\n
The result is approximately 1.34<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The Z-scores that bound the middle 82% of the area under the standard normal curve are -1.34<\/strong> and 1.34<\/strong>.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
\n
A Z-score represents the number of standard deviations a data point is from the mean in a standard normal distribution.<\/li>\n\n\n\n
The middle 82% means that 9% of the area is on the lower tail, and 9% on the upper tail, leaving 82% in the middle. By using the invNorm<\/code> function, we are finding the Z-scores that correspond to the cumulative probabilities of 0.09 (lower bound) and 0.91 (upper bound).<\/li>\n\n\n\n
The TI-84 calculator uses the cumulative distribution function (CDF) to return these Z-scores.<\/li>\n<\/ul>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Use the TI-84 calculator to find the Z-scores that bound the middle 82% of the area under the standard normal curve. Enter the answers in ascending order and round to two decimal places. The Z-scores for the given area are [insert correct values here] and [insert correct values here]. The Correct Answer and Explanation is: […]<\/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-246573","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246573","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=246573"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246573\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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