{"id":42994,"date":"2025-06-29T12:39:40","date_gmt":"2025-06-29T12:39:40","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42994"},"modified":"2025-06-29T12:39:41","modified_gmt":"2025-06-29T12:39:41","slug":"find-the-z-scores-for-which-70-of-the-distributions-area-lies-between-z-and-z_-0-7-1-036-0-036-0-35","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-z-scores-for-which-70-of-the-distributions-area-lies-between-z-and-z_-0-7-1-036-0-036-0-35\/","title":{"rendered":"Find the Z-scores for which 70% of the distribution’s area lies between ~Z and Z_ 0.7 1.036 -0.036 0.35"},"content":{"rendered":"\n


Find the Z-scores for which 70% of the distribution’s area lies between ~Z and Z_ 0.7 1.036 -0.036 0.35<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the z-scores for which 70% of the distribution’s area lies between \u2212Z-Z\u2212Z and ZZZ, you need to understand that the area between these two z-scores represents the middle 70% of the normal distribution. This means that 15% of the total area lies in each of the two tails beyond these z-scores (because 100% – 70% = 30%, and this is split between the two tails).<\/p>\n\n\n\n

Step 1: Determine the cumulative area.<\/h3>\n\n\n\n

Since the total area between the two z-scores is 70%, the cumulative area to the left of ZZZ is 0.85 (because 70% of the area is between \u2212Z-Z\u2212Z and ZZZ, and half of the remaining 30% is in the left tail). Therefore, the cumulative area to the left of the positive z-score is 0.85. The cumulative area to the left of the negative z-score is 0.15 (because it’s symmetric).<\/p>\n\n\n\n

Step 2: Find the corresponding z-scores.<\/h3>\n\n\n\n

You can use a standard normal distribution table or a Z-table to find the z-scores corresponding to these cumulative areas.<\/p>\n\n\n\n

    \n
  • The z-score for a cumulative area of 0.85 is approximately 1.036.<\/li>\n\n\n\n
  • The z-score for a cumulative area of 0.15 is approximately -1.036.<\/li>\n<\/ul>\n\n\n\n

    Step 3: Conclusion.<\/h3>\n\n\n\n

    Thus, the z-scores for which 70% of the distribution’s area lies between them are approximately \u22121.036-1.036\u22121.036 and 1.0361.0361.036.<\/p>\n\n\n\n

    These z-scores are symmetric because the normal distribution is symmetric, and they represent the points beyond which 15% of the area lies in each tail. This means that between \u22121.036-1.036\u22121.036 and 1.0361.0361.036, you capture 70% of the total area under the normal curve.<\/p>\n\n\n\n

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

    Find the Z-scores for which 70% of the distribution’s area lies between ~Z and Z_ 0.7 1.036 -0.036 0.35 The Correct Answer and Explanation is: To find the z-scores for which 70% of the distribution’s area lies between \u2212Z-Z\u2212Z and ZZZ, you need to understand that the area between these two z-scores represents the middle […]<\/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-42994","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42994","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=42994"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42994\/revisions"}],"predecessor-version":[{"id":42996,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42994\/revisions\/42996"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}