{"id":22753,"date":"2025-06-16T21:47:18","date_gmt":"2025-06-16T21:47:18","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=22753"},"modified":"2025-06-16T21:47:30","modified_gmt":"2025-06-16T21:47:30","slug":"what-percentage-of-scores-are-between-65-and-75","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-percentage-of-scores-are-between-65-and-75\/","title":{"rendered":"What percentage of scores are between 65 and 75"},"content":{"rendered":"\n

What percentage of scores are between 65 and 75?<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

To answer \u201cWhat percentage of scores are between 65 and 75?\u201d<\/strong>, we need some additional information\u2014most commonly, the distribution of the scores, their mean (average), and standard deviation. Usually, this question relates to scores that follow a normal distribution<\/strong> (a bell curve).<\/p>\n\n\n\n

\n\n\n\n

Step 1: Assume Normal Distribution<\/h3>\n\n\n\n

Let’s assume the scores are normally distributed with a mean (\u03bc)<\/strong> and standard deviation (\u03c3)<\/strong> given or implied. For example:<\/p>\n\n\n\n

    \n
  • Mean (\u03bc) = 70<\/li>\n\n\n\n
  • Standard deviation (\u03c3) = 5<\/li>\n<\/ul>\n\n\n\n

    These values are common assumptions if none are provided.<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Convert Scores to Z-Scores<\/h3>\n\n\n\n

    A Z-score<\/strong> tells how many standard deviations a data point is from the mean: Z=X\u2212\u03bc\u03c3Z = \\frac{X – \\mu}{\\sigma}<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • XX = the score<\/li>\n\n\n\n
    • \u03bc\\mu = mean<\/li>\n\n\n\n
    • \u03c3\\sigma = standard deviation<\/li>\n<\/ul>\n\n\n\n

      Calculate the Z-scores for 65 and 75:<\/p>\n\n\n\n

        \n
      • For 65:<\/li>\n<\/ul>\n\n\n\n

        Z65=65\u2212705=\u221255=\u22121Z_{65} = \\frac{65 – 70}{5} = \\frac{-5}{5} = -1<\/p>\n\n\n\n

          \n
        • For 75:<\/li>\n<\/ul>\n\n\n\n

          Z75=75\u2212705=55=1Z_{75} = \\frac{75 – 70}{5} = \\frac{5}{5} = 1<\/p>\n\n\n\n

          \n\n\n\n

          Step 3: Use the Standard Normal Distribution Table<\/h3>\n\n\n\n

          The Z-table (or standard normal distribution table) shows the area (percentage) under the normal curve up to a certain Z-score.<\/p>\n\n\n\n

            \n
          • Area to the left of Z = 1 is approximately 0.8413 (84.13%)<\/li>\n\n\n\n
          • Area to the left of Z = -1 is approximately 0.1587 (15.87%)<\/li>\n<\/ul>\n\n\n\n
            \n\n\n\n

            Step 4: Calculate the Percentage Between 65 and 75<\/h3>\n\n\n\n

            The percentage between the two Z-scores is: P(65<X<75)=P(Z<1)\u2212P(Z<\u22121)=0.8413\u22120.1587=0.6826P(65 < X < 75) = P(Z < 1) – P(Z < -1) = 0.8413 – 0.1587 = 0.6826<\/p>\n\n\n\n

            Convert to percentage: 0.6826\u00d7100=68.26%0.6826 \\times 100 = 68.26\\%<\/p>\n\n\n\n

            \n\n\n\n

            Final Answer:<\/h3>\n\n\n\n

            Approximately 68.26% of the scores lie between 65 and 75, assuming the mean is 70 and standard deviation is 5 in a normal distribution.<\/strong><\/p>\n\n\n\n

            \n\n\n\n

            Explanation:<\/h3>\n\n\n\n

            This result reflects the empirical rule<\/strong> (68-95-99.7 rule) of normal distributions, which states:<\/p>\n\n\n\n

              \n
            • About 68% of data fall within \u00b11 standard deviation<\/strong> of the mean.<\/li>\n\n\n\n
            • About 95% within \u00b12 standard deviations.<\/li>\n\n\n\n
            • About 99.7% within \u00b13 standard deviations.<\/li>\n<\/ul>\n\n\n\n

              In this problem, the scores from 65 to 75 are exactly one standard deviation below and above the mean (70), so the percentage of scores in that range is about 68%.<\/p>\n\n\n\n

              If the mean and standard deviation are different or unknown, you would need those values to calculate the exact percentage.<\/p>\n","protected":false},"excerpt":{"rendered":"

              What percentage of scores are between 65 and 75? The correct answer and explanation is: To answer \u201cWhat percentage of scores are between 65 and 75?\u201d, we need some additional information\u2014most commonly, the distribution of the scores, their mean (average), and standard deviation. Usually, this question relates to scores that follow a normal distribution (a […]<\/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-22753","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22753","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=22753"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22753\/revisions"}],"predecessor-version":[{"id":22754,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22753\/revisions\/22754"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}