{"id":234885,"date":"2025-06-14T14:22:03","date_gmt":"2025-06-14T14:22:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234885"},"modified":"2025-06-14T14:22:05","modified_gmt":"2025-06-14T14:22:05","slug":"the-birth-weight-of-full-term-babies-is-known-to-be-normally-distributed-a-bell-shape-with-a-mean-of-3400-grams-and-a-standard-deviation-of-505-grams","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/the-birth-weight-of-full-term-babies-is-known-to-be-normally-distributed-a-bell-shape-with-a-mean-of-3400-grams-and-a-standard-deviation-of-505-grams\/","title":{"rendered":"The birth weight of full-term babies is known to be normally distributed (a bell shape) with a mean of 3400 grams and a standard deviation of 505 grams."},"content":{"rendered":"\n<p>The birth weight of full-term babies is known to be normally distributed (a bell shape) with a mean of 3400 grams and a standard deviation of 505 grams. Use the empirical rule to answer the following: Approximately 95% of the full-term babies will fall between what weights? Approximately what percent of the full-term babies will weigh more than 4410 grams (about 9 pounds 11 1\/2 oz)?<\/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><strong>Correct Answers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Approximately 95% of full-term babies<\/strong> will weigh <strong>between 2390 grams and 4410 grams<\/strong>.<\/li>\n\n\n\n<li><strong>Approximately 2.5% of full-term babies<\/strong> will weigh <strong>more than 4410 grams<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (without using the word &#8220;we&#8221;):<\/strong><\/p>\n\n\n\n<p>The empirical rule, also called the <strong>68-95-99.7 rule<\/strong>, provides a quick estimate of the spread of data in a normal distribution. According to this rule:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>About <strong>68%<\/strong> of the data falls within <strong>1 standard deviation<\/strong> of the mean.<\/li>\n\n\n\n<li>About <strong>95%<\/strong> of the data falls within <strong>2 standard deviations<\/strong> of the mean.<\/li>\n\n\n\n<li>About <strong>99.7%<\/strong> of the data falls within <strong>3 standard deviations<\/strong> of the mean.<\/li>\n<\/ul>\n\n\n\n<p>The <strong>mean<\/strong> birth weight of full-term babies is <strong>3400 grams<\/strong>, and the <strong>standard deviation<\/strong> is <strong>505 grams<\/strong>.<\/p>\n\n\n\n<p>To find the range where approximately 95% of the birth weights fall:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calculate <strong>2 standard deviations<\/strong> below and above the mean.\n<ul class=\"wp-block-list\">\n<li>Lower bound: 3400 \u2212 (2 \u00d7 505) = 3400 \u2212 1010 = <strong>2390 grams<\/strong><\/li>\n\n\n\n<li>Upper bound: 3400 + (2 \u00d7 505) = 3400 + 1010 = <strong>4410 grams<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>So, approximately <strong>95%<\/strong> of full-term babies will have birth weights between <strong>2390 grams and 4410 grams<\/strong>.<\/p>\n\n\n\n<p>Next, to determine the percentage of babies who weigh <strong>more than 4410 grams<\/strong>, consider that 4410 grams is exactly <strong>2 standard deviations above the mean<\/strong>. In a normal distribution, about <strong>95%<\/strong> of the data lies between \u22122\u03c3 and +2\u03c3, which leaves <strong>5%<\/strong> in the two tails of the distribution (outside that range). These two tails are split evenly:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>About <strong>2.5%<\/strong> lie <strong>above<\/strong> the +2\u03c3 mark.<\/li>\n\n\n\n<li>About <strong>2.5%<\/strong> lie <strong>below<\/strong> the \u22122\u03c3 mark.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, approximately <strong>2.5% of full-term babies<\/strong> will weigh <strong>more than 4410 grams<\/strong>, which is equivalent to <strong>about 9 pounds 11\u00bd ounces<\/strong>.<\/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-banner8-519.jpeg\" alt=\"\" class=\"wp-image-234886\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The birth weight of full-term babies is known to be normally distributed (a bell shape) with a mean of 3400 grams and a standard deviation of 505 grams. Use the empirical rule to answer the following: Approximately 95% of the full-term babies will fall between what weights? Approximately what percent of the full-term babies will [&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-234885","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234885","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=234885"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234885\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234885"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234885"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234885"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}