{"id":274130,"date":"2025-07-28T05:32:46","date_gmt":"2025-07-28T05:32:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=274130"},"modified":"2025-07-28T05:32:49","modified_gmt":"2025-07-28T05:32:49","slug":"a-computer-instructor-found-out-that-on-average-his-students-complete-their-modules-in-120-hours-with-a-standard-deviation-of-10-hours","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/28\/a-computer-instructor-found-out-that-on-average-his-students-complete-their-modules-in-120-hours-with-a-standard-deviation-of-10-hours\/","title":{"rendered":"A computer instructor found out that on average, his students complete their modules in 120 hours with a standard deviation of 10 hours"},"content":{"rendered":"\n<p>A computer instructor found out that on average, his students complete their modules in 120 hours with a standard deviation of 10 hours. Assuming that his data are normally distributed, what is the probability that a randomly selected student will complete his module in 100 to 140 hours? Write your answer correct to four decimal places, as in 0.1234.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we will use the normal distribution and Z-scores to calculate the probability that a randomly selected student will complete their module in 100 to 140 hours.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the Mean and Standard Deviation<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mean (\u03bc) = 120 hours<\/li>\n\n\n\n<li>Standard deviation (\u03c3) = 10 hours<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Convert the Hours to Z-Scores<\/h3>\n\n\n\n<p>We need to convert the values of 100 and 140 hours to Z-scores using the following formula: Z=X\u2212\u03bc\u03c3Z = \\frac{X &#8211; \\mu}{\\sigma}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>XX is the value (either 100 or 140 hours)<\/li>\n\n\n\n<li>\u03bc\\mu is the mean (120 hours)<\/li>\n\n\n\n<li>\u03c3\\sigma is the standard deviation (10 hours)<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Z-score for 100 hours:<\/h4>\n\n\n\n<p>Z=100\u221212010=\u22122010=\u22122Z = \\frac{100 &#8211; 120}{10} = \\frac{-20}{10} = -2<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Z-score for 140 hours:<\/h4>\n\n\n\n<p>Z=140\u221212010=2010=2Z = \\frac{140 &#8211; 120}{10} = \\frac{20}{10} = 2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Look Up the Z-Scores in the Standard Normal Table<\/h3>\n\n\n\n<p>We now look up the Z-scores in the standard normal distribution table or use a calculator.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The probability corresponding to a Z-score of -2 is approximately 0.0228.<\/li>\n\n\n\n<li>The probability corresponding to a Z-score of 2 is approximately 0.9772.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the Probability Between 100 and 140 Hours<\/h3>\n\n\n\n<p>To find the probability that a student will complete their module between 100 and 140 hours, subtract the probability corresponding to Z = -2 from the probability corresponding to Z = 2: P(100\u2264X\u2264140)=P(Z=2)\u2212P(Z=\u22122)=0.9772\u22120.0228=0.9544P(100 \\leq X \\leq 140) = P(Z = 2) &#8211; P(Z = -2) = 0.9772 &#8211; 0.0228 = 0.9544<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The probability that a randomly selected student will complete their module in 100 to 140 hours is <strong>0.9544<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A computer instructor found out that on average, his students complete their modules in 120 hours with a standard deviation of 10 hours. Assuming that his data are normally distributed, what is the probability that a randomly selected student will complete his module in 100 to 140 hours? Write your answer correct to four decimal [&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-274130","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274130","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=274130"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/274130\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=274130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=274130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=274130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}