{"id":5199,"date":"2022-08-18T21:13:48","date_gmt":"2022-08-18T21:13:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=5199"},"modified":"2022-08-18T21:19:49","modified_gmt":"2022-08-18T21:19:49","slug":"9c-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/9c-coreq\/","title":{"raw":"9C Coreq","rendered":"9C Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to find probabilities\u00a0 and percentiles of a normal distribution.\r\n\r\nEmpirical Rule\r\n\r\nWhen a variable has a normal distribution, the Empirical Rule will apply:\r\n<ul>\r\n \t<li>About 68% of the values will fall within one standard deviation from the mean.<\/li>\r\n \t<li>About 95% of the values will fall within two standard deviations from the mean.<\/li>\r\n \t<li>About 99.7% of the values will fall within three standard deviations from the mean.<\/li>\r\n<\/ul>\r\nThe Scholastic Aptitude Test (SAT) is an assessment designed to evaluate a student\u2019s\u00a0 college-specific skills. SAT scores tend to follow an approximate normal distribution with a mean of 1060 and a standard deviation of 195.[footnote]National Center for Education Statistics. (2019). <em>Table 226.40 SAT mean scores of high school seniors, standard deviations, and percentage of the graduating class taking the SAT, by state: 2017, 2018, and 2019<\/em>. https:\/\/nces.ed.gov\/programs\/digest\/d19\/tables\/dt19_226.40.asp[\/footnote]\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 1<\/h3>\r\nUse the Empirical Rule to complete the following sentences.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>About 68% of SAT scores will fall between _____ and _____.<\/li>\r\n \t<li>About 95% of SAT scores will fall between _____ and _____.<\/li>\r\n \t<li>About 99.7% of SAT scores will fall between _____ and _____.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 2<\/h3>\r\nUse your answers from Question 1 to draw a graph of the distribution of SAT scores\u00a0 with the middle 68%, 95%, and 99.7% marked. Clearly label your x-axis.\r\n\r\n<\/div>\r\nNormal Percentiles\r\n\r\nThe American College Test (ACT) is another assessment designed to evaluate a\u00a0 student\u2019s college-specific skills. ACT scores tend to follow an approximate normal\u00a0 distribution with a mean of 20.8 and a standard deviation of 5.8.[footnote]National Center for Education Statistics. (2019). <em>Table 226.50 Number and percentage of graduates taking the ACT test; average scores and standard deviations, by sex and race\/ethnicity; and percentage of test takers with selected composite scores and planned fields of postsecondary study: selected years, 1995 through 2018.<\/em> https:\/\/nces.ed.gov\/programs\/digest\/d19\/tables\/dt19_226.50.asp[\/footnote]\r\n\r\nA percentile of a distribution is the value at which a certain percentage falls below that\u00a0 value. For example, the 95th percentile of ACT scores would be the score at which 95%\u00a0 of students score below.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 3<\/h3>\r\nJane scored a 30 on the ACT.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Calculate the associated normal probability to complete the following\u00a0 sentence:\r\nJane scored above _____% of all students taking the ACT.<\/li>\r\n \t<li>What percentile is an ACT score of 30?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 4<\/h3>\r\nFind the 30th percentile of ACT scores.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 5<\/h3>\r\nFind the associated percentiles to complete the following sentence: 75% of students score between _____ and ______ on the ACT.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Question 6<\/h3>\r\nJulie took the ACT and scored 28. Tim took the SAT and scored 1200. Calculate the\u00a0 z-score for each student to determine whether Tim or Julie scored in a higher\u00a0 percentile.\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<p>In the next preview assignment and in the next class, you will need to find probabilities\u00a0 and percentiles of a normal distribution.<\/p>\n<p>Empirical Rule<\/p>\n<p>When a variable has a normal distribution, the Empirical Rule will apply:<\/p>\n<ul>\n<li>About 68% of the values will fall within one standard deviation from the mean.<\/li>\n<li>About 95% of the values will fall within two standard deviations from the mean.<\/li>\n<li>About 99.7% of the values will fall within three standard deviations from the mean.<\/li>\n<\/ul>\n<p>The Scholastic Aptitude Test (SAT) is an assessment designed to evaluate a student\u2019s\u00a0 college-specific skills. SAT scores tend to follow an approximate normal distribution with a mean of 1060 and a standard deviation of 195.<a class=\"footnote\" title=\"National Center for Education Statistics. (2019). Table 226.40 SAT mean scores of high school seniors, standard deviations, and percentage of the graduating class taking the SAT, by state: 2017, 2018, and 2019. https:\/\/nces.ed.gov\/programs\/digest\/d19\/tables\/dt19_226.40.asp\" id=\"return-footnote-5199-1\" href=\"#footnote-5199-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 1<\/h3>\n<p>Use the Empirical Rule to complete the following sentences.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>About 68% of SAT scores will fall between _____ and _____.<\/li>\n<li>About 95% of SAT scores will fall between _____ and _____.<\/li>\n<li>About 99.7% of SAT scores will fall between _____ and _____.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 2<\/h3>\n<p>Use your answers from Question 1 to draw a graph of the distribution of SAT scores\u00a0 with the middle 68%, 95%, and 99.7% marked. Clearly label your x-axis.<\/p>\n<\/div>\n<p>Normal Percentiles<\/p>\n<p>The American College Test (ACT) is another assessment designed to evaluate a\u00a0 student\u2019s college-specific skills. ACT scores tend to follow an approximate normal\u00a0 distribution with a mean of 20.8 and a standard deviation of 5.8.<a class=\"footnote\" title=\"National Center for Education Statistics. (2019). Table 226.50 Number and percentage of graduates taking the ACT test; average scores and standard deviations, by sex and race\/ethnicity; and percentage of test takers with selected composite scores and planned fields of postsecondary study: selected years, 1995 through 2018. https:\/\/nces.ed.gov\/programs\/digest\/d19\/tables\/dt19_226.50.asp\" id=\"return-footnote-5199-2\" href=\"#footnote-5199-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>A percentile of a distribution is the value at which a certain percentage falls below that\u00a0 value. For example, the 95th percentile of ACT scores would be the score at which 95%\u00a0 of students score below.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Question 3<\/h3>\n<p>Jane scored a 30 on the ACT.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Calculate the associated normal probability to complete the following\u00a0 sentence:<br \/>\nJane scored above _____% of all students taking the ACT.<\/li>\n<li>What percentile is an ACT score of 30?<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 4<\/h3>\n<p>Find the 30th percentile of ACT scores.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 5<\/h3>\n<p>Find the associated percentiles to complete the following sentence: 75% of students score between _____ and ______ on the ACT.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Question 6<\/h3>\n<p>Julie took the ACT and scored 28. Tim took the SAT and scored 1200. Calculate the\u00a0 z-score for each student to determine whether Tim or Julie scored in a higher\u00a0 percentile.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5199-1\">National Center for Education Statistics. (2019). <em>Table 226.40 SAT mean scores of high school seniors, standard deviations, and percentage of the graduating class taking the SAT, by state: 2017, 2018, and 2019<\/em>. https:\/\/nces.ed.gov\/programs\/digest\/d19\/tables\/dt19_226.40.asp <a href=\"#return-footnote-5199-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-5199-2\">National Center for Education Statistics. (2019). <em>Table 226.50 Number and percentage of graduates taking the ACT test; average scores and standard deviations, by sex and race\/ethnicity; and percentage of test takers with selected composite scores and planned fields of postsecondary study: selected years, 1995 through 2018.<\/em> https:\/\/nces.ed.gov\/programs\/digest\/d19\/tables\/dt19_226.50.asp <a href=\"#return-footnote-5199-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":7,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5199","chapter","type-chapter","status-publish","hentry"],"part":5175,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5199\/revisions"}],"predecessor-version":[{"id":5202,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5199\/revisions\/5202"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5175"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5199\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5199"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5199"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5199"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}