{"id":5144,"date":"2022-08-18T17:11:31","date_gmt":"2022-08-18T17:11:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5144"},"modified":"2022-08-18T17:16:17","modified_gmt":"2022-08-18T17:16:17","slug":"8e-practice","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/8e-practice\/","title":{"raw":"8E Practice","rendered":"8E Practice"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to understand that every value of a variable\u00a0 with a normal distribution has a corresponding z-score for the standard normal\u00a0 distribution, and you will use technology to calculate probabilities for normally distributed\u00a0 variables. You will also need to use technology to calculate a corresponding value of a\u00a0 random variable for a given percentile and use the Empirical Rule to identify values that\u00a0 are usual and unusual.\r\n
\r\n

Question 1<\/h3>\r\nAccording to the Empirical Rule, what percentage of values will be contained\u00a0 between one standard deviation below the mean and one standard deviation above\u00a0 the mean?\r\n
    \r\n \t
  1. 34%<\/li>\r\n \t
  2. 50%<\/li>\r\n \t
  3. 68%<\/li>\r\n<\/ol>\r\n\"\"\r\n\r\n<\/div>\r\nQuestions 2 and 3: Go to https:\/\/dcmathpathways.shinyapps.io\/NormalDist\/<\/a> to open the DCMP Normal Distribution tool.\r\n
    \r\n

    Question 2<\/h3>\r\nAccording to the Empirical Rule, what percentage of values will be contained\u00a0 between one standard deviation below the mean and one standard deviation above\u00a0 the mean?\r\n\r\nWhich of the following describes what the numbers on the following graph (1, 2, 3, etc.) represent?\r\n
      \r\n \t
    1. Z-scores<\/li>\r\n \t
    2. Standard Deviation<\/li>\r\n \t
    3. Number of occurrences<\/li>\r\n \t
    4. Probability<\/li>\r\n<\/ol>\r\nHint: Review the standard normal curve.\r\n\r\n<\/div>\r\n
      \r\n

      Question 3<\/h3>\r\nAt the top of the DCMP Normal Distribution tool, choose the Find Probability tab.\r\n
        \r\n \t
      1. Let\u2019s find the exact probability that a normally distributed random variable is\u00a0 within one standard deviation of the mean.\r\nTo find the probability that a random variable will be between two specified\u00a0 values, set \u201cType of Probability\u201d to \u201cInterval: [latex] P(a < X < b) [\/latex].\u201d\r\nWhat is the probability that a random variable that has a standard normal\u00a0 distribution will be between \u22121 and 1?\r\nHint: Use the \u201cValue of a\u201d box to set your lower value and the \u201cValue of b\u201d box to set\u00a0 your upper value. Remember that the shaded part of the graph represents the\u00a0 probability.<\/li>\r\n \t
      2. What do you notice about your answer for Part a?\u00a0Hint: Remember the Empirical Rule.<\/li>\r\n<\/ol>\r\n<\/div>\r\nQuestions 4 and 5: Continue using the DCMP Normal Distribution tool to complete any\u00a0 necessary calculations.\r\n
        \r\n

        Question 4<\/h3>\r\nRecall Question 3 from Practice Assignment 8.D. The average body temperature for\u00a0 healthy adults is 98.2\u00b0F with a standard deviation of 0.73\u00b0F.\r\n
          \r\n \t
        1. What is the probability a randomly selected healthy adult will have a\u00a0 temperature below 98.6\u00b0F? Write your answer as a proportion. Include 4\u00a0 decimal places in your answer.\r\nHint: Use the lower tail probability.<\/li>\r\n \t
        2. What is the probability a randomly selected healthy adult will have a\u00a0 temperature above 100.4\u00b0F?\r\n\r\nHint: Use the upper tail probability.<\/li>\r\n \t
        3. A fever is considered medically significant if body temperature reaches\u00a0 100.4\u00b0F. What do you observe about this temperature? Do you think this\u00a0 temperature is medically significant?\r\n\r\nHint: Think about z-scores. How many standard deviations above the mean is this\u00a0 temperature?<\/li>\r\n<\/ol>\r\n<\/div>\r\n
          \r\n

          Question 5<\/h3>\r\nOne thousand high school juniors take a standardized exam. The distribution of\u00a0 student scores approximates a normal distribution with an average score of 68.4 and\u00a0 a standard deviation of 6.8.\r\n
            \r\n \t
          1. What percentage of students passed the exam with a score of at least 65? Hint: Use the upper tail probability.<\/li>\r\n \t
          2. Students who scored between 55 and 65 are given the chance to take the\u00a0 exam again to improve their scores. What percentage of students will have\u00a0 the chance to retake the exam?\r\n\r\nHint: Use the interval probability.<\/li>\r\n \t
          3. Fill in the blanks. Round to the nearest hundredth.\r\n\r\nApproximately 68% of all scores are between _____ and _____.\r\n\r\nApproximately 95% of all scores are between _____ and _____.\r\n\r\nApproximately 99.7% of all scores are between _____ and _____.\r\n\r\nHint: Remember the Empirical Rule.<\/li>\r\n \t
          4. On their score reports, students are told how their scores compare to other\u00a0 students\u2019 scores. For example, a student might be told that they scored\u00a0 better than 80% of their peers. We can use this information to estimate the\u00a0 students\u2019 raw scores.\r\nAt the top of the DCMP Normal Distribution tool, choose the Find\r\n\r\nPercentile\/Quantile tab. Set the mean to 68.4 and the standard deviation to\u00a0 6.8. Use the tool to complete the following table. Round to the nearest\u00a0 hundredth.<\/li>\r\n \t
          5. \r\n
            \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Student Scored\r\n\r\nBetter Than [latex] x [\/latex]% of\u00a0 Peers<\/td>\r\nApproximate\r\n\r\nRaw Score<\/td>\r\n<\/tr>\r\n
            5%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
            20%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
            80%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
            99%<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nHint: Use the lower tail option to calculate the percentile.<\/li>\r\n<\/ol>\r\n<\/div>\r\n ","rendered":"

            Preparing for the next class<\/p>\n

            In the next in-class activity, you will need to understand that every value of a variable\u00a0 with a normal distribution has a corresponding z-score for the standard normal\u00a0 distribution, and you will use technology to calculate probabilities for normally distributed\u00a0 variables. You will also need to use technology to calculate a corresponding value of a\u00a0 random variable for a given percentile and use the Empirical Rule to identify values that\u00a0 are usual and unusual.<\/p>\n

            \n

            Question 1<\/h3>\n

            According to the Empirical Rule, what percentage of values will be contained\u00a0 between one standard deviation below the mean and one standard deviation above\u00a0 the mean?<\/p>\n

              \n
            1. 34%<\/li>\n
            2. 50%<\/li>\n
            3. 68%<\/li>\n<\/ol>\n

              \"\"<\/p>\n<\/div>\n

              Questions 2 and 3: Go to https:\/\/dcmathpathways.shinyapps.io\/NormalDist\/<\/a> to open the DCMP Normal Distribution tool.<\/p>\n

              \n

              Question 2<\/h3>\n

              According to the Empirical Rule, what percentage of values will be contained\u00a0 between one standard deviation below the mean and one standard deviation above\u00a0 the mean?<\/p>\n

              Which of the following describes what the numbers on the following graph (1, 2, 3, etc.) represent?<\/p>\n

                \n
              1. Z-scores<\/li>\n
              2. Standard Deviation<\/li>\n
              3. Number of occurrences<\/li>\n
              4. Probability<\/li>\n<\/ol>\n

                Hint: Review the standard normal curve.<\/p>\n<\/div>\n

                \n

                Question 3<\/h3>\n

                At the top of the DCMP Normal Distribution tool, choose the Find Probability tab.<\/p>\n

                  \n
                1. Let\u2019s find the exact probability that a normally distributed random variable is\u00a0 within one standard deviation of the mean.
                  \nTo find the probability that a random variable will be between two specified\u00a0 values, set \u201cType of Probability\u201d to \u201cInterval: [latex]P(a < X < b)[\/latex].\u201d\nWhat is the probability that a random variable that has a standard normal\u00a0 distribution will be between \u22121 and 1?\nHint: Use the \u201cValue of a\u201d box to set your lower value and the \u201cValue of b\u201d box to set\u00a0 your upper value. Remember that the shaded part of the graph represents the\u00a0 probability.<\/li>\n
                2. What do you notice about your answer for Part a?\u00a0Hint: Remember the Empirical Rule.<\/li>\n<\/ol>\n<\/div>\n

                  Questions 4 and 5: Continue using the DCMP Normal Distribution tool to complete any\u00a0 necessary calculations.<\/p>\n

                  \n

                  Question 4<\/h3>\n

                  Recall Question 3 from Practice Assignment 8.D. The average body temperature for\u00a0 healthy adults is 98.2\u00b0F with a standard deviation of 0.73\u00b0F.<\/p>\n

                    \n
                  1. What is the probability a randomly selected healthy adult will have a\u00a0 temperature below 98.6\u00b0F? Write your answer as a proportion. Include 4\u00a0 decimal places in your answer.
                    \nHint: Use the lower tail probability.<\/li>\n
                  2. What is the probability a randomly selected healthy adult will have a\u00a0 temperature above 100.4\u00b0F?\n

                    Hint: Use the upper tail probability.<\/li>\n

                  3. A fever is considered medically significant if body temperature reaches\u00a0 100.4\u00b0F. What do you observe about this temperature? Do you think this\u00a0 temperature is medically significant?\n

                    Hint: Think about z-scores. How many standard deviations above the mean is this\u00a0 temperature?<\/li>\n<\/ol>\n<\/div>\n

                    \n

                    Question 5<\/h3>\n

                    One thousand high school juniors take a standardized exam. The distribution of\u00a0 student scores approximates a normal distribution with an average score of 68.4 and\u00a0 a standard deviation of 6.8.<\/p>\n

                      \n
                    1. What percentage of students passed the exam with a score of at least 65? Hint: Use the upper tail probability.<\/li>\n
                    2. Students who scored between 55 and 65 are given the chance to take the\u00a0 exam again to improve their scores. What percentage of students will have\u00a0 the chance to retake the exam?\n

                      Hint: Use the interval probability.<\/li>\n

                    3. Fill in the blanks. Round to the nearest hundredth.\n

                      Approximately 68% of all scores are between _____ and _____.<\/p>\n

                      Approximately 95% of all scores are between _____ and _____.<\/p>\n

                      Approximately 99.7% of all scores are between _____ and _____.<\/p>\n

                      Hint: Remember the Empirical Rule.<\/li>\n

                    4. On their score reports, students are told how their scores compare to other\u00a0 students\u2019 scores. For example, a student might be told that they scored\u00a0 better than 80% of their peers. We can use this information to estimate the\u00a0 students\u2019 raw scores.
                      \nAt the top of the DCMP Normal Distribution tool, choose the Find<\/p>\n

                      Percentile\/Quantile tab. Set the mean to 68.4 and the standard deviation to\u00a0 6.8. Use the tool to complete the following table. Round to the nearest\u00a0 hundredth.<\/li>\n

                    5. \n
                      \n\n\n\n\n\n\n\n
                      Student Scored<\/p>\n

                      Better Than [latex]x[\/latex]% of\u00a0 Peers<\/td>\n

                      		Approximate<\/p>\n

                      Raw Score<\/td>\n<\/tr>\n

                      5%<\/td>\n<\/td>\n<\/tr>\n
                      20%<\/td>\n<\/td>\n<\/tr>\n
                      80%<\/td>\n<\/td>\n<\/tr>\n
                      99%<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

                      Hint: Use the lower tail option to calculate the percentile.<\/li>\n<\/ol>\n<\/div>\n

                       <\/p>\n","protected":false},"author":574340,"menu_order":15,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5144","chapter","type-chapter","status-publish","hentry"],"part":4997,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5144","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5144\/revisions"}],"predecessor-version":[{"id":5148,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5144\/revisions\/5148"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4997"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5144\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5144"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5144"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5144"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5144"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}