{"id":1167,"date":"2016-07-20T11:33:20","date_gmt":"2016-07-20T15:33:20","guid":{"rendered":"https:\/\/sites.berry.edu\/vbissonnette\/?page_id=1167"},"modified":"2017-01-10T13:46:07","modified_gmt":"2017-01-10T18:46:07","slug":"illustrate-the-normal-distribution","status":"publish","type":"page","link":"https:\/\/sites.berry.edu\/vbissonnette\/index\/stats-homework\/documentation\/illustrate-the-normal-distribution\/","title":{"rendered":"Illustrate the Normal Distribution"},"content":{"rendered":"<h3>Homework Problem #1<\/h3>\n<p>You are working with the standard normal distribution (i.e., a distribution of z scores). \u00a0What proportion of the scores in this distribution would be greater than a score of +0.50?<\/p>\n<p>In <em>Stats Homework<\/em>, pull down the\u00a0<strong>Probability<\/strong> menu, choose\u00a0<strong>Illustrate Areas in a Distribution<\/strong>, and then choose\u00a0<strong>Illustrate Areas in the Normal Distribution<\/strong> (if running the stand alone program, you will not need to do this). Here is the user dialog you will be working with:<\/p>\n<p><a href=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1178\" src=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm1.png\" alt=\"norm1\" width=\"995\" height=\"594\" srcset=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm1.png 995w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm1-300x179.png 300w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm1-768x458.png 768w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm1-260x155.png 260w\" sizes=\"auto, (max-width: 995px) 100vw, 995px\" \/><\/a><\/p>\n<p>Click &#8220;Find the tail area,&#8221; enter a score of .50, and press the enter key or click on the &#8220;Illustrate&#8221; button. \u00a0Here are the results:<\/p>\n<p><a href=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1237\" src=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm2.png\" alt=\"\" width=\"667\" height=\"530\" srcset=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm2.png 667w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm2-300x238.png 300w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm2-260x207.png 260w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\" \/><\/a><\/p>\n<p>You can see that the area greater than a z score of .50 is equal to .3085. \u00a0Now, click the other options to see what results you will get. \u00a0Also, explore the\u00a0<strong>Image Options<\/strong>. \u00a0You can resize this plot, change the title or labels, copy it to your clipboard, and save it to a file.<\/p>\n<hr \/>\n<h3>Homework Problem #2<\/h3>\n<p>Which two z scores will define the central 95% of a standard normal distribution?<\/p>\n<p>Pull down the <strong>Analysis Options<\/strong> menu, and choose\u00a0<strong>Find Scores in the Normal Distribution<\/strong>. \u00a0Click &#8220;Find scores for the central proportion,&#8221; enter .95 as your score, and then press enter or click the illustrate button. \u00a0Here are the results:<\/p>\n<p><a href=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1238\" src=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm3.png\" alt=\"\" width=\"667\" height=\"530\" srcset=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm3.png 667w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm3-300x238.png 300w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm3-260x207.png 260w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\" \/><\/a><\/p>\n<p>You can see that z scores of -1.96 and +1.96 define the central 95% of a standard normal distribution. \u00a0Now, click the other options here to see the other types of results that you can produce.<\/p>\n<hr \/>\n<h3>Homework Problem #3<\/h3>\n<p>You are working with a normal distribution of IQ scores, which have a mean of 100 and a standard deviation of 15. \u00a0What percentage of scores will be found between a score of 115 and a score of 130?<\/p>\n<p>Press the &#8220;Reset&#8221; button. \u00a0Now, pull down the\u00a0<strong>Analysis Options<\/strong> menu, and choose\u00a0<strong>Some other Normal Distribution<\/strong>. \u00a0Also, click\u00a0the &#8220;Find the area between two scores&#8221; option. \u00a0You will have to enter four values:<\/p>\n<p><a href=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm4.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1176\" src=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2016\/07\/norm4.png\" alt=\"norm4\" width=\"995\" height=\"594\" \/><\/a><\/p>\n<p>Enter a mean of 100, and a standard deviation of 15. \u00a0Then, enter your two scores &#8212; enter 115 for the first one and 130 for the second (note that you must enter the lower score as your first score). \u00a0Now, press enter or click &#8220;illustrate.&#8221; \u00a0Here are the results.<\/p>\n<p><a href=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm5.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1239\" src=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm5.png\" alt=\"\" width=\"667\" height=\"530\" srcset=\"https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm5.png 667w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm5-300x238.png 300w, https:\/\/sites.berry.edu\/vbissonnette\/wp-content\/uploads\/sites\/21\/2017\/01\/norm5-260x207.png 260w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\" \/><\/a><\/p>\n<p>You can see that this area is equal to .1359. \u00a0Notice that the program will fill in the z scores that you have to compute to solve this problem,<\/p>\n<hr \/>\n<p><a href=\"https:\/\/sites.berry.edu\/vbissonnette\/index\/stats-homework\/documentation\/\">Return to Table of Contents<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Homework Problem #1 You are working with the standard normal distribution (i.e., a distribution of z scores). \u00a0What proportion of the scores in this distribution would be greater than a [&hellip;]<\/p>\n","protected":false},"author":34,"featured_media":0,"parent":282,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-container-style":"default","site-container-layout":"default","site-sidebar-layout":"default","site-transparent-header":"default","disable-article-header":"default","disable-site-header":"default","disable-site-footer":"default","disable-content-area-spacing":"default","footnotes":""},"class_list":["post-1167","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/1167","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/users\/34"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/comments?post=1167"}],"version-history":[{"count":9,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/1167\/revisions"}],"predecessor-version":[{"id":1240,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/1167\/revisions\/1240"}],"up":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/282"}],"wp:attachment":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/media?parent=1167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}