{"id":215032,"date":"2025-05-16T07:16:14","date_gmt":"2025-05-16T07:16:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=215032"},"modified":"2025-05-16T07:16:16","modified_gmt":"2025-05-16T07:16:16","slug":"elephants-have-the-longest-pregnancy-of-all-mammals","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/16\/elephants-have-the-longest-pregnancy-of-all-mammals\/","title":{"rendered":"Elephants have the longest pregnancy of all mammals."},"content":{"rendered":"\n<p>Elephants have the longest pregnancy of all mammals. One species of elephant has a mean gestation period of 525 days and standard deviation of 32 days. These pregnancy lengths can be modeled by a normal distribution. What is the probability that a randomly selected elephant of this species has a pregnancy that lasts between 500 and 550 days? There is a 25% chance that an elephant from this species will have a pregnancy that lasts longer than <strong>__<\/strong> days.<\/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>We are given the following information about elephant gestation:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mean (\u03bc) = 525 days<\/li>\n\n\n\n<li>Standard deviation (\u03c3) = 32 days<\/li>\n\n\n\n<li>The distribution is <strong>normal<\/strong><\/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\"><strong>Part 1: Probability that a pregnancy lasts between 500 and 550 days<\/strong><\/h3>\n\n\n\n<p>We want:<br><strong>P(500 \u2264 X \u2264 550)<\/strong><br>To find this probability, we convert raw scores (X-values) into <strong>z-scores<\/strong> using: z=X\u2212\u03bc\u03c3z = \\frac{X &#8211; \\mu}{\\sigma}<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Z-score for 500 days<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>z=500\u221252532=\u22122532\u2248\u22120.78z = \\frac{500 &#8211; 525}{32} = \\frac{-25}{32} \\approx -0.78<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Z-score for 550 days<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>z=550\u221252532=2532\u22480.78z = \\frac{550 &#8211; 525}{32} = \\frac{25}{32} \\approx 0.78<\/p>\n\n\n\n<p>Using a standard normal distribution table (or calculator):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P(Z \u2264 0.78) \u2248 0.7823<\/strong><\/li>\n\n\n\n<li><strong>P(Z \u2264 -0.78) \u2248 0.2177<\/strong><\/li>\n<\/ul>\n\n\n\n<p>P(500\u2264X\u2264550)=P(Z\u22640.78)\u2212P(Z\u2264\u22120.78)=0.7823\u22120.2177=0.5646P(500 \u2264 X \u2264 550) = P(Z \u2264 0.78) &#8211; P(Z \u2264 -0.78) = 0.7823 &#8211; 0.2177 = 0.5646<\/p>\n\n\n\n<p>\u2705 <strong>Answer: The probability is approximately 0.5646 or 56.46%.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Part 2: There is a 25% chance that a pregnancy lasts longer than how many days?<\/strong><\/h3>\n\n\n\n<p>We are looking for the <strong>X-value<\/strong> where the upper tail of the normal distribution contains 25% of the values.<\/p>\n\n\n\n<p>That means: P(X&gt;x)=0.25\u21d2P(X\u2264x)=0.75P(X &gt; x) = 0.25 \\Rightarrow P(X \u2264 x) = 0.75<\/p>\n\n\n\n<p>Using a <strong>z-table<\/strong>, the z-score corresponding to <strong>0.75 cumulative probability<\/strong> is approximately <strong>z = 0.674<\/strong>.<\/p>\n\n\n\n<p>Now convert z back to an X-value using: X=\u03bc+z\u03c3=525+(0.674)(32)\u2248525+21.57=546.57X = \\mu + z\\sigma = 525 + (0.674)(32) \\approx 525 + 21.57 = 546.57<\/p>\n\n\n\n<p>\u2705 <strong>Answer: About 546.57 days<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Summary<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Probability of a pregnancy lasting between 500 and 550 days is ~56.46%.<\/strong><\/li>\n\n\n\n<li><strong>There is a 25% chance a pregnancy lasts more than ~546.57 da<\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Elephants have the longest pregnancy of all mammals. One species of elephant has a mean gestation period of 525 days and standard deviation of 32 days. These pregnancy lengths can be modeled by a normal distribution. What is the probability that a randomly selected elephant of this species has a pregnancy that lasts between 500 [&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-215032","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215032","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=215032"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215032\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=215032"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=215032"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=215032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}