{"id":214,"date":"2019-11-07T22:14:09","date_gmt":"2019-11-07T22:14:09","guid":{"rendered":"https:\/\/pressbooks.usnh.edu\/math502\/chapter\/exercises-6\/"},"modified":"2023-03-24T14:26:22","modified_gmt":"2023-03-24T14:26:22","slug":"exercises-6","status":"publish","type":"chapter","link":"https:\/\/pressbooks.usnh.edu\/mth402\/chapter\/exercises-6\/","title":{"raw":"Exercises","rendered":"Exercises"},"content":{"raw":"

Review Exercises<\/strong><\/h2>\n
    \n \t
  1. \n
      \n \t
    1. Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a\u00a0score between 600 and 700?<\/li>\n \t
    2. Considering a full-grown show-quality male Siberian Husky has a mean weight of 52.5 lbs, with SD of 7.5\u00a0lbs, how common are male huskies in the 37.5\u201345 lbs range?<\/li>\n \t
    3. A population \u00b5 = 125, and \u03c3 = 25, how common are values in the 100 \u2013 150 range?<\/li>\n \t
    4. Population \u00b5 = 0.0025 and \u03c3 = 0.0005, how common are values between 0.0025 and 0.0030?<\/li>\n \t
    5. A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans\u00a0with between 11 and 11.5 oz of soda?<\/span><\/li>\n \t
    6. \u00b5 = 0.0025 and \u03c3 = 0.0005, how common are values between 0.0045 and 0.005?<\/li>\n \t
    7. If a population \u00b5 = 1130 and \u03c3 = 5, how common are values between 0 and 1100?<\/li>\n \t
    8. Assuming population \u00b5 = 1130 and \u03c3 = 5, how common are values between 1125 and 1135?<\/li>\n \t
    9. The American Robin Redbreast has a mean weight of 77 g, with a standard deviation of 6 g. How common\u00a0are Robins in the 59 g\u221271 g range?<\/li>\n \t
    10. Population \u00b5 = 0.25% and \u03c3 = 0.05%, how common are values between 0.35% and 0.45%?<\/li>\n \t
    11. Population \u00b5 = 156.5 and \u03c3 = 0.25, how common are values between 155 and 156?<\/li>\n<\/ol>\n

      Assume all distributions to be normal or approximately normal, and calculate percentages using the 68\u221295\u221299.7 rule.<\/h4>\n
        \n \t
      1. \n
          \n \t
        1. Given mean 63 and standard deviation of 168, find the approximate percentage of the distribution that lies between \u2212105 and 567.<\/li>\n \t
        2. Approximately what percent of a normal distribution is between 2 standard deviations and 3 standard deviations from the mean?<\/li>\n \t
        3. Given standard deviation of 74 and mean of 124, approximately what percentage of the values are greater than 198?<\/li>\n \t
        4. Given \u03c3 = 39 and \u00b5 = 101, approximately what percentage of the values are less than 23?<\/li>\n \t
        5. Given mean 92 and standard deviation 189, find the approximate percentage of the distribution that lies between \u2212286 and 470.<\/li>\n \t
        6. Approximately what percent of a normal distribution lies between \u00b5 + 1\u03c3 and \u00b5 + 2\u03c3?<\/li>\n \t
        7. Given standard deviation of 113 and mean 81, approximately what percentage of the values are less than \u2212145?<\/li>\n \t
        8. Given mean 23 and standard deviation 157, find the approximate percentage of the distribution that lies between 23 and 337.<\/li>\n \t
        9. Given \u03c3 = 3 and \u00b5 = 84, approximately what percentage of the values are greater than 90?<\/li>\n \t
        10. Approximately what percent of a normal distribution is between \u00b5 and \u00b5+1\u03c3?<\/li>\n \t
        11. Given mean 118 and standard deviation 145, find the approximate percentage of the distribution that lies between \u221227 and 118.<\/li>\n \t
        12. Given standard deviation of 81 and mean 67, approximately what percentage of values are greater than 310?<\/li>\n \t
        13. Approximately what percent of a normal distribution is less than 2 standard deviations from the mean?<\/li>\n \t
        14. Given \u00b5 + 1\u03c3 = 247 and \u00b5 + 2\u03c3 = 428, find the approximate percentage of the distribution that lies between 66 and 428.<\/li>\n \t
        15. Given \u00b5 \u2212 1\u03c3 = \u2212131 and \u00b5 + 1\u03c3 = 233, approximately what percentage of the values are greater than \u2212495?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

          The following problems are based on section 6.3 in your text.<\/h4>\n
            \n \t
          1. \n
              \n \t
            1. \n
                \n \t
              1. Given a distribution with a mean of 70 and standard deviation of 62, find a value with a z-score of \u22121.82.<\/li>\n \t
              2. What does a z-score of 3.4 mean?<\/li>\n \t
              3. Given a distribution with a mean of 60 and standard deviation of 98, find the z-score of 120.76.<\/li>\n \t
              4. Given a distribution with a mean of 60 and standard deviation of 21, find a value with a z-score of 2.19.<\/li>\n \t
              5. Find the z-score of 187.37, given a distribution with a mean of 185 and standard deviation of 1.<\/li>\n \t
              6. What does a z-score of \u22123.8 mean?<\/li>\n \t
              7. Find the z-score of 125.18, given a distribution with a mean of 101 and standard deviation of 62.<\/li>\n \t
              8. Given a distribution with a mean of 117 and standard deviation of 42, find a value with a z-score of \u22120.94.<\/li>\n \t
              9. Given a distribution with a mean of 126 and standard deviation of 100, find a value with a z-score of \u22120.75.<\/li>\n \t
              10. Find the z-score of 264.16, given \u00b5 = 188 and \u03c3 = 64.<\/li>\n \t
              11. Find a value with a z-score of \u22120.2, given \u00b5 = 145 and \u03c3 = 56.<\/li>\n \t
              12. Find the z-score of 89.79 given \u00b5 = 10 and \u03c3 = 79.<\/li>\n \t
              13. Find the probabilities, use the table from the lesson above.<\/li>\n \t
              14. What is the probability of a z-score less than +2.02?<\/li>\n \t
              15. What is the probability of a z-score greater than +2.02?<\/li>\n \t
              16. What is the probability of a z-score less than \u22121.97?<\/li>\n \t
              17. What is the probability of a z-score greater than \u22121.97?<\/li>\n \t
              18. What is the probability of a z-score less than +0.09?<\/li>\n \t
              19. What is the probability of a z-score less than \u22120.02?<\/li>\n \t
              20. What is P<\/em>(Z<\/em> < 1.71)?<\/li>\n \t
              21. What is P<\/em>(Z<\/em> > 2.22)?<\/li>\n \t
              22. What is P<\/em>(Z<\/em> < \u22121.19)?<\/li>\n \t
              23. What is P<\/em>(Z<\/em> > \u22122.71)?<\/li>\n \t
              24. What is P<\/em>(Z<\/em> < 3.71)?<\/li>\n \t
              25. What is the probability of the random occurrence of a value greater than 56 from a normally distributed\u00a0population with mean 62 and standard deviation 4.5?<\/li>\n \t
              26. What is the probability of a value of 329 or greater, assuming a normally distributed set with mean 290 and\u00a0standard deviation 32?<\/li>\n \t
              27. What is the probability of getting a value below 1.2 from the random output of a normally distributed set with \u00b5 = 2.6 and \u03c3 = .9?<\/li>\n \t
              28. Find the probabilities, use the table from the lesson or an online resource.<\/li>\n \t
              29. What is the probability of a z-score between +1.99 and +2.02?<\/li>\n \t
              30. What is the probability of a z-score between \u22121.99 and +2.02?<\/li>\n \t
              31. What is the probability of a z-score between \u22121.20 and \u22121.97?<\/li>\n \t
              32. What is the probability of a z-score between +2.33 and \u22120.97?<\/li>\n \t
              33. What is the probability of a z-score greater than +0.09?<\/li>\n \t
              34. What is the probability of a z-score greater than \u22120.02?<\/li>\n \t
              35. What is P<\/em>(1.42 < Z<\/em> < 2.01)?<\/li>\n \t
              36. What is P<\/em>(1.77 < Z<\/em> < 2.22)?<\/li>\n \t
              37. What is P<\/em>(\u22122.33 < Z<\/em> < \u22121.19)?<\/li>\n \t
              38. What is P<\/em>(\u22123.01 < Z<\/em> < \u22120.71)?<\/li>\n \t
              39. What is P<\/em>(2.66 < Z<\/em> < 3.71)?<\/li>\n \t
              40. What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed\u00a0population with mean 62 and standard deviation 4.5?<\/li>\n \t
              41. What is the probability of a value between 301 and 329, assuming a normally distributed set with mean 290\u00a0and standard deviation 32?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n

                Attributions<\/p>\nThis chapter contains material taken from Math in Society<\/em> (on OpenTextBookStore<\/a>) by David Lippman, and is used under a CC Attribution-Share Alike 3.0 United States<\/a>\u00a0(CC BY-SA 3.0 US) license.\n","rendered":"

                Review Exercises<\/strong><\/h2>\n
                  \n
                1. \n
                    \n
                  1. Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a\u00a0score between 600 and 700?<\/li>\n
                  2. Considering a full-grown show-quality male Siberian Husky has a mean weight of 52.5 lbs, with SD of 7.5\u00a0lbs, how common are male huskies in the 37.5\u201345 lbs range?<\/li>\n
                  3. A population \u00b5 = 125, and \u03c3 = 25, how common are values in the 100 \u2013 150 range?<\/li>\n
                  4. Population \u00b5 = 0.0025 and \u03c3 = 0.0005, how common are values between 0.0025 and 0.0030?<\/li>\n
                  5. A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans\u00a0with between 11 and 11.5 oz of soda?<\/span><\/li>\n
                  6. \u00b5 = 0.0025 and \u03c3 = 0.0005, how common are values between 0.0045 and 0.005?<\/li>\n
                  7. If a population \u00b5 = 1130 and \u03c3 = 5, how common are values between 0 and 1100?<\/li>\n
                  8. Assuming population \u00b5 = 1130 and \u03c3 = 5, how common are values between 1125 and 1135?<\/li>\n
                  9. The American Robin Redbreast has a mean weight of 77 g, with a standard deviation of 6 g. How common\u00a0are Robins in the 59 g\u221271 g range?<\/li>\n
                  10. Population \u00b5 = 0.25% and \u03c3 = 0.05%, how common are values between 0.35% and 0.45%?<\/li>\n
                  11. Population \u00b5 = 156.5 and \u03c3 = 0.25, how common are values between 155 and 156?<\/li>\n<\/ol>\n

                    Assume all distributions to be normal or approximately normal, and calculate percentages using the 68\u221295\u221299.7 rule.<\/h4>\n
                      \n
                    1. \n
                        \n
                      1. Given mean 63 and standard deviation of 168, find the approximate percentage of the distribution that lies between \u2212105 and 567.<\/li>\n
                      2. Approximately what percent of a normal distribution is between 2 standard deviations and 3 standard deviations from the mean?<\/li>\n
                      3. Given standard deviation of 74 and mean of 124, approximately what percentage of the values are greater than 198?<\/li>\n
                      4. Given \u03c3 = 39 and \u00b5 = 101, approximately what percentage of the values are less than 23?<\/li>\n
                      5. Given mean 92 and standard deviation 189, find the approximate percentage of the distribution that lies between \u2212286 and 470.<\/li>\n
                      6. Approximately what percent of a normal distribution lies between \u00b5 + 1\u03c3 and \u00b5 + 2\u03c3?<\/li>\n
                      7. Given standard deviation of 113 and mean 81, approximately what percentage of the values are less than \u2212145?<\/li>\n
                      8. Given mean 23 and standard deviation 157, find the approximate percentage of the distribution that lies between 23 and 337.<\/li>\n
                      9. Given \u03c3 = 3 and \u00b5 = 84, approximately what percentage of the values are greater than 90?<\/li>\n
                      10. Approximately what percent of a normal distribution is between \u00b5 and \u00b5+1\u03c3?<\/li>\n
                      11. Given mean 118 and standard deviation 145, find the approximate percentage of the distribution that lies between \u221227 and 118.<\/li>\n
                      12. Given standard deviation of 81 and mean 67, approximately what percentage of values are greater than 310?<\/li>\n
                      13. Approximately what percent of a normal distribution is less than 2 standard deviations from the mean?<\/li>\n
                      14. Given \u00b5 + 1\u03c3 = 247 and \u00b5 + 2\u03c3 = 428, find the approximate percentage of the distribution that lies between 66 and 428.<\/li>\n
                      15. Given \u00b5 \u2212 1\u03c3 = \u2212131 and \u00b5 + 1\u03c3 = 233, approximately what percentage of the values are greater than \u2212495?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                        The following problems are based on section 6.3 in your text.<\/h4>\n
                          \n
                        1. \n
                            \n
                          1. \n
                              \n
                            1. Given a distribution with a mean of 70 and standard deviation of 62, find a value with a z-score of \u22121.82.<\/li>\n
                            2. What does a z-score of 3.4 mean?<\/li>\n
                            3. Given a distribution with a mean of 60 and standard deviation of 98, find the z-score of 120.76.<\/li>\n
                            4. Given a distribution with a mean of 60 and standard deviation of 21, find a value with a z-score of 2.19.<\/li>\n
                            5. Find the z-score of 187.37, given a distribution with a mean of 185 and standard deviation of 1.<\/li>\n
                            6. What does a z-score of \u22123.8 mean?<\/li>\n
                            7. Find the z-score of 125.18, given a distribution with a mean of 101 and standard deviation of 62.<\/li>\n
                            8. Given a distribution with a mean of 117 and standard deviation of 42, find a value with a z-score of \u22120.94.<\/li>\n
                            9. Given a distribution with a mean of 126 and standard deviation of 100, find a value with a z-score of \u22120.75.<\/li>\n
                            10. Find the z-score of 264.16, given \u00b5 = 188 and \u03c3 = 64.<\/li>\n
                            11. Find a value with a z-score of \u22120.2, given \u00b5 = 145 and \u03c3 = 56.<\/li>\n
                            12. Find the z-score of 89.79 given \u00b5 = 10 and \u03c3 = 79.<\/li>\n
                            13. Find the probabilities, use the table from the lesson above.<\/li>\n
                            14. What is the probability of a z-score less than +2.02?<\/li>\n
                            15. What is the probability of a z-score greater than +2.02?<\/li>\n
                            16. What is the probability of a z-score less than \u22121.97?<\/li>\n
                            17. What is the probability of a z-score greater than \u22121.97?<\/li>\n
                            18. What is the probability of a z-score less than +0.09?<\/li>\n
                            19. What is the probability of a z-score less than \u22120.02?<\/li>\n
                            20. What is P<\/em>(Z<\/em> < 1.71)?<\/li>\n
                            21. What is P<\/em>(Z<\/em> > 2.22)?<\/li>\n
                            22. What is P<\/em>(Z<\/em> < \u22121.19)?<\/li>\n
                            23. What is P<\/em>(Z<\/em> > \u22122.71)?<\/li>\n
                            24. What is P<\/em>(Z<\/em> < 3.71)?<\/li>\n
                            25. What is the probability of the random occurrence of a value greater than 56 from a normally distributed\u00a0population with mean 62 and standard deviation 4.5?<\/li>\n
                            26. What is the probability of a value of 329 or greater, assuming a normally distributed set with mean 290 and\u00a0standard deviation 32?<\/li>\n
                            27. What is the probability of getting a value below 1.2 from the random output of a normally distributed set with \u00b5 = 2.6 and \u03c3 = .9?<\/li>\n
                            28. Find the probabilities, use the table from the lesson or an online resource.<\/li>\n
                            29. What is the probability of a z-score between +1.99 and +2.02?<\/li>\n
                            30. What is the probability of a z-score between \u22121.99 and +2.02?<\/li>\n
                            31. What is the probability of a z-score between \u22121.20 and \u22121.97?<\/li>\n
                            32. What is the probability of a z-score between +2.33 and \u22120.97?<\/li>\n
                            33. What is the probability of a z-score greater than +0.09?<\/li>\n
                            34. What is the probability of a z-score greater than \u22120.02?<\/li>\n
                            35. What is P<\/em>(1.42 < Z<\/em> < 2.01)?<\/li>\n
                            36. What is P<\/em>(1.77 < Z<\/em> < 2.22)?<\/li>\n
                            37. What is P<\/em>(\u22122.33 < Z<\/em> < \u22121.19)?<\/li>\n
                            38. What is P<\/em>(\u22123.01 < Z<\/em> < \u22120.71)?<\/li>\n
                            39. What is P<\/em>(2.66 < Z<\/em> < 3.71)?<\/li>\n
                            40. What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed\u00a0population with mean 62 and standard deviation 4.5?<\/li>\n
                            41. What is the probability of a value between 301 and 329, assuming a normally distributed set with mean 290\u00a0and standard deviation 32?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                              Attributions<\/p>\n

                              This chapter contains material taken from Math in Society<\/em> (on OpenTextBookStore<\/a>) by David Lippman, and is used under a CC Attribution-Share Alike 3.0 United States<\/a>\u00a0(CC BY-SA 3.0 US) license.
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