{"id":198,"date":"2016-10-26T01:10:31","date_gmt":"2016-10-26T05:10:31","guid":{"rendered":"http:\/\/blog.fitnyc.edu\/professorshloming\/?p=198"},"modified":"2016-10-26T01:10:31","modified_gmt":"2016-10-26T05:10:31","slug":"how-do-i-go-from-a-z-score-to-a-percent","status":"publish","type":"post","link":"https:\/\/blog.fitnyc.edu\/professorshloming\/2016\/10\/26\/how-do-i-go-from-a-z-score-to-a-percent\/","title":{"rendered":"How do I go from a z-score to a percent?"},"content":{"rendered":"<p>How do I go from a z-score to a percent?<\/p>\n<p>ANSWER:<\/p>\n<p><span style=\"font-weight: 400\">Our z-score does not automatically turn into a percent by multiplying by 100 and adding a percent sign. <strong>We must use the standard normal table to figure out the area and turn that into a percent! <\/strong><\/span><\/p>\n<p><span style=\"text-decoration: underline\"><span style=\"font-weight: 400\">We can go from the x &#8211; value to a z &#8211; score to the area \/ percent by using the table. <\/span><\/span><\/p>\n<p><span style=\"font-weight: 400\">We can also go backwards! We can be given an area \/ percent then by using the table find the associated \u00a0z &#8211; score and then figure out the corresponding to x &#8211; value. More on how to go backwards is in this Course FAQ post:<\/span><\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"xJMPQ8S16V\"><p><a href=\"https:\/\/blog.fitnyc.edu\/professorshloming\/2015\/03\/19\/im-having-issues-using-the-standard-normal-table-backwards-to-look-up-the-z-value-for-example-if-a-left-tail-area-0-2-how-does-z-0-84\/\">I&#8217;m having issues using the standard normal table backwards to look up the z value.    For example, \u201cIf a left tail area = 0.2 how does z= -0.84  ?\u201d<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; clip: rect(1px, 1px, 1px, 1px);\" title=\"&#8220;I&#8217;m having issues using the standard normal table backwards to look up the z value.    For example, \u201cIf a left tail area = 0.2 how does z= -0.84  ?\u201d&#8221; &#8212; COURSE FAQ: Blog for My Online Courses\" src=\"https:\/\/blog.fitnyc.edu\/professorshloming\/2015\/03\/19\/im-having-issues-using-the-standard-normal-table-backwards-to-look-up-the-z-value-for-example-if-a-left-tail-area-0-2-how-does-z-0-84\/embed\/#?secret=svdA4eZN84#?secret=xJMPQ8S16V\" data-secret=\"xJMPQ8S16V\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>Looking at Problem\u00a015-11 a \u00a0Heights. \u00a0You should have obtained z =\u00a0-1.33.\u00a0<span style=\"text-decoration: underline\"><strong>Remember\u00a0you need to always round to 2 decimal places for z scores.\u00a0<\/strong><\/span><\/p>\n<p>In this problem we are asked for the left tail area.<\/p>\n<p>Using the standard normal table (in your book or on our Course Site) we look up the area of the left tail associated with z-value of -1.33.<\/p>\n<p>The left tail area from the chart is<\/p>\n<p><a href=\"http:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-199\" src=\"http:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-828x1024.png\" alt=\"screen-shot-2016-10-26-at-1-11-35-am\" width=\"625\" height=\"773\" srcset=\"https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-828x1024.png 828w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-243x300.png 243w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-768x949.png 768w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-624x771.png 624w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-19x24.png 19w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-29x36.png 29w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM-39x48.png 39w, https:\/\/blog.fitnyc.edu\/professorshloming\/files\/2016\/10\/Screen-Shot-2016-10-26-at-1.11.35-AM.png 948w\" sizes=\"auto, (max-width: 625px) 100vw, 625px\" \/><\/a><\/p>\n<p><strong>Left tail area = .0918<\/strong><\/p>\n<p>We multiply this by 100 % to get a percent.<\/p>\n<p><span style=\"font-weight: 400\">Rounded to the nearest percent this is 9%.<\/span><\/p>\n<p>(Right tail area and other problem types can be found on the Course FAQ!)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How do I go from a z-score to a percent? ANSWER: Our z-score does not automatically turn into a percent by multiplying by 100 and adding a percent sign. We must use the standard normal table to figure out the area and turn that into [&hellip;]<\/p>\n","protected":false},"author":386,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[26127,28562],"tags":[],"class_list":["post-198","post","type-post","status-publish","format-standard","hentry","category-assignments","category-ma222"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p3ANrd-3c","_links":{"self":[{"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/posts\/198","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/users\/386"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/comments?post=198"}],"version-history":[{"count":0,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/posts\/198\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/media?parent=198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/categories?post=198"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/tags?post=198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}