{"id":1908,"date":"2021-09-15T14:46:12","date_gmt":"2021-09-15T14:46:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1908"},"modified":"2022-02-07T19:21:58","modified_gmt":"2022-02-07T19:21:58","slug":"introduction-to-using-the-central-limit-theorem","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-to-using-the-central-limit-theorem\/","title":{"raw":"Introduction to Using the Central Limit Theorem","rendered":"Introduction to Using the Central Limit Theorem"},"content":{"raw":"<h2>What you\u2019ll learn to do: use the central limit theorem to calculate probabilities and percentiles for normal and non-normal population distributions<\/h2>\r\n<img class=\"size-medium wp-image-1909 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/15144506\/pexels-pavel-danilyuk-7234226-200x300.jpg\" alt=\"A bucket of popcorn on an armrest in a movie theater\" width=\"200\" height=\"300\" \/>Movie critic ratings are uniformly distributed for many movies, because the opinions of movie critics vary widely. What is the probability that the average score is more than 80 for a recent movie for a randomly selected group of 30 movie critics? Being able to apply the central limit theorem and work with normal distribution probabilities is needed to answer this question.","rendered":"<h2>What you\u2019ll learn to do: use the central limit theorem to calculate probabilities and percentiles for normal and non-normal population distributions<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1909 alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/15144506\/pexels-pavel-danilyuk-7234226-200x300.jpg\" alt=\"A bucket of popcorn on an armrest in a movie theater\" width=\"200\" height=\"300\" \/>Movie critic ratings are uniformly distributed for many movies, because the opinions of movie critics vary widely. What is the probability that the average score is more than 80 for a recent movie for a randomly selected group of 30 movie critics? Being able to apply the central limit theorem and work with normal distribution probabilities is needed to answer this question.<\/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-1908\">\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>Bucket of Popcorn on the Armrest. <strong>Authored by<\/strong>: Pavel Danilyuk. <strong>Provided by<\/strong>: Pexels. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.pexels.com\/photo\/bucket-of-popcorn-on-the-armrest-7234226\/\">https:\/\/www.pexels.com\/photo\/bucket-of-popcorn-on-the-armrest-7234226\/<\/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":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Bucket of Popcorn on the Armrest\",\"author\":\"Pavel Danilyuk\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/bucket-of-popcorn-on-the-armrest-7234226\/\",\"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-1908","chapter","type-chapter","status-publish","hentry"],"part":262,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1908","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":2,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1908\/revisions"}],"predecessor-version":[{"id":3720,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1908\/revisions\/3720"}],"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\/1908\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1908"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1908"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1908"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}