{"id":123,"date":"2015-03-19T16:01:17","date_gmt":"2015-03-19T20:01:17","guid":{"rendered":"http:\/\/blog.fitnyc.edu\/professorshloming\/?p=123"},"modified":"2015-03-19T16:01:17","modified_gmt":"2015-03-19T20:01:17","slug":"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","status":"publish","type":"post","link":"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\/","title":{"rendered":"I’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"},"content":{"rendered":"

I’m having issues using the standard normal table backwards to look up the z value. \u00a0<\/b>For example, \u201cIf a left tail area = 0.2 how does z= -0.84 \u00a0?\u201d<\/b><\/p>\n

Step by step:<\/p>\n

Let\u2019s draw what we left tail area = .2 means.<\/p>\n

\"chart\"<\/a><\/strong><\/strong><\/p>\n

Here is a picture of the area we want, showing approximately 20% on the left. We know that there is 50% from all the way to the left to 0 so where we see z = ? looks like .2<\/p>\n

This helps us see that our z score is definitely going to be negative. I can also see that it won’t be z = -2 or z = -3 but closer to z = -1.<\/p>\n

Using the normal table backwards we look up the z-value associated with the above given area:<\/p>\n

\"Screen<\/a>
\n<\/strong><\/strong>You either use the chart in your book or the one I have on our site. It is under Learning Modules and then click on Standard Normal Table.
\n<\/strong><\/strong><\/p>\n

\u00a0<\/strong><\/strong><\/p>\n

I am going to look for the value closest to 0.2 listed for the areas.<\/p>\n

\"Screen<\/a><\/strong><\/strong><\/p>\n

\u2192 .2005<\/b> is the closest we have to .2 using this chart!<\/p>\n

\u00a0<\/strong><\/strong><\/p>\n

See the .2005 here enlarged.<\/p>\n

\"Screen<\/a><\/p>\n

<\/strong><\/strong><\/p>\n

So for the z-value we get:<\/p>\n


\nz = -0.84<\/strong><\/strong><\/p>\n

This is because you have .2005 is in the same row as -0.8 and then we match up with the column.<\/p>\n

The column is ._4<\/p>\n

\u00a0<\/strong><\/strong><\/p>\n

So the z-value we want is -0.84.<\/p>\n

\u00a0<\/strong><\/strong><\/p>\n

Just to make sure you get the idea let\u2019s look at all the areas before .2005. What would their z-scores be?<\/p>\n

\"Screen<\/a><\/strong><\/strong><\/p>\n

.2119 would be -.80<\/p>\n

.2090 would be -.81<\/p>\n

.2061 would be -.82<\/p>\n

.2033 would be -.83<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

I’m having issues using the standard normal table backwards to look up the z value. \u00a0For example, \u201cIf a left tail area = 0.2 how does z= -0.84 \u00a0?\u201d Step by step: Let\u2019s draw what we left tail area = .2 means. Here is a […]<\/p>\n","protected":false},"author":386,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_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},"jetpack_post_was_ever_published":false},"categories":[28562],"tags":[],"class_list":["post-123","post","type-post","status-publish","format-standard","hentry","category-ma222"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p3ANrd-1Z","_links":{"self":[{"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/posts\/123","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=123"}],"version-history":[{"count":0,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/posts\/123\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/media?parent=123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/categories?post=123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.fitnyc.edu\/professorshloming\/wp-json\/wp\/v2\/tags?post=123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}