{"id":1902,"date":"2021-09-15T14:34:24","date_gmt":"2021-09-15T14:34:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1902"},"modified":"2022-02-07T19:07:09","modified_gmt":"2022-02-07T19:07:09","slug":"introduction-to-the-central-limit-theorem-for-sums","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-to-the-central-limit-theorem-for-sums\/","title":{"raw":"Introduction to The Central Limit Theorem for Sums","rendered":"Introduction to The Central Limit Theorem for Sums"},"content":{"raw":"<h2>What you\u2019ll learn to do: calculate probabilities and percentiles for the sampling distribution for a sum<\/h2>\r\n<img class=\"size-medium wp-image-1903 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/15143318\/pexels-kelly-lacy-3861787-300x200.jpg\" alt=\"A peson pressing an button on an elevator. The picture just shows the. persons. hand.\" width=\"300\" height=\"200\" \/>A sign on an elevator reads \u201cMaximum Capacity 2000 pounds.\u201d Let\u2019s say that a random sample of 10 adults is taken and the total weight is calculated. What is the probability that the total weight will exceed 2000 pounds? The central limit theorem for sums is similar to the central limit for means and allows us to answer questions like this one.","rendered":"<h2>What you\u2019ll learn to do: calculate probabilities and percentiles for the sampling distribution for a sum<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1903 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/15143318\/pexels-kelly-lacy-3861787-300x200.jpg\" alt=\"A peson pressing an button on an elevator. The picture just shows the. persons. hand.\" width=\"300\" height=\"200\" \/>A sign on an elevator reads \u201cMaximum Capacity 2000 pounds.\u201d Let\u2019s say that a random sample of 10 adults is taken and the total weight is calculated. What is the probability that the total weight will exceed 2000 pounds? The central limit theorem for sums is similar to the central limit for means and allows us to answer questions like this one.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1902\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Anonymous person pressing button of lift. <strong>Authored by<\/strong>: Kelly Lacy. <strong>Provided by<\/strong>: Pexels. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.pexels.com\/photo\/anonymous-person-pressing-button-of-lift-3861787\/\">https:\/\/www.pexels.com\/photo\/anonymous-person-pressing-button-of-lift-3861787\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Anonymous person pressing button of lift\",\"author\":\"Kelly Lacy\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/anonymous-person-pressing-button-of-lift-3861787\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1902","chapter","type-chapter","status-publish","hentry"],"part":262,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1902","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1902\/revisions"}],"predecessor-version":[{"id":3715,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1902\/revisions\/3715"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/262"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1902\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1902"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1902"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1902"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1902"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}