{"id":19195,"date":"2025-06-13T13:59:59","date_gmt":"2025-06-13T13:59:59","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=19195"},"modified":"2025-06-13T14:00:07","modified_gmt":"2025-06-13T14:00:07","slug":"find-the-z-scores-that-cut-off-the-most-extreme-6-under-the-standard-normal-curve","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-z-scores-that-cut-off-the-most-extreme-6-under-the-standard-normal-curve\/","title":{"rendered":"Find the z scores that cut-off the most extreme 6% under the standard normal curve"},"content":{"rendered":"\n<p>Find the z scores that cut-off the most extreme 6% under the standard normal curve. a. \u00b11.55 b. \u00b11.88 c. \u00b10.52 d. \u00b10.51<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is: <strong>b. \u00b11.88<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (Approximately 300 Words):<\/h3>\n\n\n\n<p>In statistics, a <strong>z-score<\/strong> represents how many standard deviations a data point is from the mean of a standard normal distribution, which has a mean of 0 and a standard deviation of 1. The <strong>&#8220;most extreme 6%&#8221;<\/strong> refers to the outer 6% of the distribution \u2014 that is, 3% in each tail (both left and right) of the standard normal curve.<\/p>\n\n\n\n<p>To find the z-scores that cut off the most extreme 6%, we look for the values where <strong>3% of the area lies in the lower tail<\/strong> (left side) and <strong>3% lies in the upper tail<\/strong> (right side). This means we want to find the z-scores that leave <strong>94% (100% &#8211; 6%)<\/strong> of the data in the center of the curve, so <strong>3% lies below the lower bound<\/strong> and <strong>3% lies above the upper bound<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Steps:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>We want to find the z-scores such that the <strong>area to the left is 0.03<\/strong> for the lower bound and <strong>0.97 (1 &#8211; 0.03)<\/strong> for the upper bound.<\/li>\n\n\n\n<li>Using a <strong>z-table<\/strong> or statistical software, we look for the z-score corresponding to <strong>0.03 cumulative probability<\/strong>.<\/li>\n\n\n\n<li>The z-score for 0.03 is approximately <strong>-1.88<\/strong>.<\/li>\n\n\n\n<li>Because the normal distribution is symmetric, the corresponding upper z-score is <strong>+1.88<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>So, the two z-scores that cut off the most extreme 6% (3% in each tail) are approximately <strong>\u00b11.88<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total extreme area: 6%<\/li>\n\n\n\n<li>Each tail: 3%<\/li>\n\n\n\n<li>Central area: 94%<\/li>\n\n\n\n<li>Corresponding z-scores: \u00b11.88<\/li>\n<\/ul>\n\n\n\n<p>These values represent the cut-off points beyond which lie the most unusual 6% of observations in a standard normal distribution \u2014 often used in hypothesis testing and confidence interval calculations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the z scores that cut-off the most extreme 6% under the standard normal curve. a. \u00b11.55 b. \u00b11.88 c. \u00b10.52 d. \u00b10.51 The correct answer and explanation is: The correct answer is: b. \u00b11.88 Explanation (Approximately 300 Words): In statistics, a z-score represents how many standard deviations a data point is from the mean [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-19195","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19195","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=19195"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19195\/revisions"}],"predecessor-version":[{"id":19196,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19195\/revisions\/19196"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}