{"id":5150,"date":"2022-08-18T17:31:43","date_gmt":"2022-08-18T17:31:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5150"},"modified":"2022-08-18T17:46:55","modified_gmt":"2022-08-18T17:46:55","slug":"8f-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/8f-coreq\/","title":{"raw":"8F Coreq","rendered":"8F Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to be able to\u00a0 evaluate formulas used to find the mean and standard deviation of a binomial\u00a0 experiment, create continuous intervals using the [latex] \\pm [\/latex] symbol, and translate intervals in\u00a0 context to probability notation.\r\n\r\nCommute Time\r\n\r\nEach year, the United States Census Bureau puts out a survey called The American\u00a0 Community Survey.[footnote]United States Census Bureau. (2021, July 9). American Community Survey Data<\/em>. https:\/\/www.census.gov\/programs-surveys\/acs\/data.html[\/footnote] This survey provides information about the social and economic\u00a0 needs of your community. Responses to this survey help provide local and national\u00a0 leaders with the information they need for planning and programs.\r\n
\r\n

Question 1<\/h3>\r\nOne of the questions in the survey asks about the time (in minutes) it takes to\u00a0 commute to work. Is this value discrete or continuous?\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\nSuppose the commuting times reported were between 0 and 150 minutes. Think\u00a0 about the time it takes for a person to commute to work as a random variable.\r\n
    \r\n \t
  1. What values can the variable have?<\/li>\r\n \t
  2. Can you list all of the values of the variable (all possible commute times)?\u00a0 Explain.<\/li>\r\n \t
  3. What are the units of the random variable (commute time)?<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n

    Question 3<\/h3>\r\nIn the upcoming in-class activity, you will be dealing with translating intervals in\u00a0 context to notation. This is necessary for calculating purposes. Also, you need to be\u00a0 comfortable with identifying values that would be located within an interval.\r\n\r\nComplete the following table where the information in the first column represents the inequality using inequality notation, the second column expresses the inequality in\u00a0 words, and the third column lists examples of values that can be found within the\u00a0 interval. In the second column, use language such as between, at most, no more\u00a0 than, up to, at least, etc. that is commonly used in probability to describe\u00a0 inequalities.\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Notation<\/td>\r\nTranslation<\/td>\r\nExample of Values Within the\u00a0 Interval<\/td>\r\n<\/tr>\r\n
    [latex] X < 25 [\/latex]<\/td>\r\n[latex] X [\/latex] is fewer than 25<\/td>\r\n22, 27.8, 15.5<\/td>\r\n<\/tr>\r\n
    [latex] X \\geq 45 [\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n[latex] X [\/latex] is between 60 and 75, not inclusive<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    [latex] X > 120 [\/latex]<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
    \r\n

    Question 4<\/h3>\r\nIn the next in-class activity, you will also need to be able to translate intervals in\u00a0 context to notation. Although you may have practiced this concept before, the more\u00a0 problems you practice, the more comfortable you will become with the various ways\u00a0 to describe inequalities.\r\n\r\nComplete the missing phrase, inequalities, and interpretation in the following table.\u00a0 Use [latex] X [\/latex] to represent the random variable.\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Phrase<\/td>\r\nInequality<\/td>\r\nExample of Values Within the\u00a0 Interval<\/td>\r\n<\/tr>\r\n
    A heart rate of\u00a0 at least 80\r\n\r\nbeats per\r\n\r\nminute (bpm)<\/td>\r\n<\/td>\r\nIf a heart rate is at least 80 bpm, it\u00a0 means that it can be 80, 81, 82,\u00a0 \u2026bpm.<\/td>\r\n<\/tr>\r\n
    A commute\r\n\r\ntime of less\r\n\r\nthan 48\r\n\r\nminutes<\/td>\r\n[latex] 0 < X < 48 [\/latex]<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n[latex] X \\leq 70 [\/latex]<\/td>\r\nIf the speed is no more than 70 miles\u00a0 per hour (mph), it means that it can be\u00a0 anywhere from 0 mph up to and\u00a0 including 70 mph.<\/td>\r\n<\/tr>\r\n
    A temperature\u00a0 above 100.2 is\u00a0 considered a\u00a0 fever for\r\n\r\nCOVID-19.<\/td>\r\n<\/td>\r\nIf a temperature above 100.2 is\u00a0 considered a fever for COVID-19, it\u00a0 means that it can be any value greater\u00a0 than 100.2. This value does not\u00a0 include 100.2.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
    \r\n

    Question 5<\/h3>\r\nUse probability notation to represent the following statements. Use [latex] X [\/latex] to represent the random variable.\r\n
      \r\n \t
    1. The probability that the commute time will be less than 30 minutes<\/li>\r\n \t
    2. The probability that the temperature will be above 100.2\u00b0 F<\/li>\r\n \t
    3. A heart rate of at least 80 bpm<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      \r\n

      Question 6<\/h3>\r\nYou will need to be able to check criteria to determine whether or not a normal distribution can be used to approximate probabilities of a binomial distribution using the following inequalities: [latex] np > 10 \\mbox{ and } n(1 \u2013 p) > 10 [\/latex].\r\n
        \r\n \t
      1. Suppose you know that [latex] n = 10 \\mbox{ and } p = 0.90 [\/latex]. Is [latex] np > 10 \\mbox{ AND } n(1 \u2013 p)[\/latex]?<\/li>\r\n \t
      2. If [latex] n = 490 \\mbox{ and } p = 0.64 [\/latex], are both [latex] np > 10 \\mbox{ and } n(1 \u2013 p) > 10 [\/latex]?<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 7<\/h3>\r\nIn probability theory, a continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution. We do this by adjusting the discrete whole numbers in a binomial distribution so that any individual value, X, is represented in the normal distribution by the interval form:\r\n\r\n[latex] X - 0.5 \\mbox{ to } X + 0.5 [\/latex]\r\n
          \r\n \t
        1. If [latex] X = 158 [\/latex] , find [latex] X \\pm 0.5 [\/latex].<\/li>\r\n \t
        2. Describe the interval from Part a using interval notation.<\/li>\r\n \t
        3. Shade the area that represents the interval you created in Part B using the following number line.\r\n\"\"<\/li>\r\n<\/ol>\r\n<\/div>\r\n
          \r\n

          Question 8<\/h3>\r\nIn In-Class Activity 8.C, you were introduced to finding the mean of a binomial distribution. The following formulas can be used to find the mean ([latex] \\mu [\/latex]) and standard deviation ([latex] \\sigma [\/latex]) of a binomial random variable:\r\n\r\n[latex] \\mu = np \\mbox{ and } \\sigma = \\sqrt{np(1-p)} [\/latex]\r\n\r\nSuppose [latex] n = 178 \\mbox{ and } p = 0.17 [\/latex].\r\n
            \r\n \t
          1. Find [latex] \\mu [\/latex]. Round your answer to the nearest whole number.<\/li>\r\n \t
          2. Find [latex] \\sigma [\/latex]. Round your answer to the nearest whole number.<\/li>\r\n<\/ol>\r\n<\/div>\r\n ","rendered":"

            In the next preview assignment and in the next class, you will need to be able to\u00a0 evaluate formulas used to find the mean and standard deviation of a binomial\u00a0 experiment, create continuous intervals using the [latex]\\pm[\/latex] symbol, and translate intervals in\u00a0 context to probability notation.<\/p>\n

            Commute Time<\/p>\n

            Each year, the United States Census Bureau puts out a survey called The American\u00a0 Community Survey.[1]<\/sup><\/a> This survey provides information about the social and economic\u00a0 needs of your community. Responses to this survey help provide local and national\u00a0 leaders with the information they need for planning and programs.<\/p>\n

            \n

            Question 1<\/h3>\n

            One of the questions in the survey asks about the time (in minutes) it takes to\u00a0 commute to work. Is this value discrete or continuous?<\/p>\n<\/div>\n

            \n

            Question 2<\/h3>\n

            Suppose the commuting times reported were between 0 and 150 minutes. Think\u00a0 about the time it takes for a person to commute to work as a random variable.<\/p>\n

              \n
            1. What values can the variable have?<\/li>\n
            2. Can you list all of the values of the variable (all possible commute times)?\u00a0 Explain.<\/li>\n
            3. What are the units of the random variable (commute time)?<\/li>\n<\/ol>\n<\/div>\n
              \n

              Question 3<\/h3>\n

              In the upcoming in-class activity, you will be dealing with translating intervals in\u00a0 context to notation. This is necessary for calculating purposes. Also, you need to be\u00a0 comfortable with identifying values that would be located within an interval.<\/p>\n

              Complete the following table where the information in the first column represents the inequality using inequality notation, the second column expresses the inequality in\u00a0 words, and the third column lists examples of values that can be found within the\u00a0 interval. In the second column, use language such as between, at most, no more\u00a0 than, up to, at least, etc. that is commonly used in probability to describe\u00a0 inequalities.<\/p>\n

              \n\n\n\n\n\n\n\n\n
              Notation<\/td>\nTranslation<\/td>\nExample of Values Within the\u00a0 Interval<\/td>\n<\/tr>\n
              [latex]X < 25[\/latex]<\/td>\n[latex]X[\/latex] is fewer than 25<\/td>\n22, 27.8, 15.5<\/td>\n<\/tr>\n
              [latex]X \\geq 45[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
              <\/td>\n[latex]X[\/latex] is between 60 and 75, not inclusive<\/td>\n<\/td>\n<\/tr>\n
              <\/td>\n<\/td>\n<\/td>\n<\/tr>\n
              [latex]X > 120[\/latex]<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
              \n

              Question 4<\/h3>\n

              In the next in-class activity, you will also need to be able to translate intervals in\u00a0 context to notation. Although you may have practiced this concept before, the more\u00a0 problems you practice, the more comfortable you will become with the various ways\u00a0 to describe inequalities.<\/p>\n

              Complete the missing phrase, inequalities, and interpretation in the following table.\u00a0 Use [latex]X[\/latex] to represent the random variable.<\/p>\n

              \n\n\n\n\n\n\n\n
              Phrase<\/td>\nInequality<\/td>\nExample of Values Within the\u00a0 Interval<\/td>\n<\/tr>\n
              A heart rate of\u00a0 at least 80<\/p>\n

              beats per<\/p>\n

              minute (bpm)<\/td>\n

              		<\/td>\nIf a heart rate is at least 80 bpm, it\u00a0 means that it can be 80, 81, 82,\u00a0 \u2026bpm.<\/td>\n<\/tr>\n
              A commute<\/p>\n

              time of less<\/p>\n

              than 48<\/p>\n

              minutes<\/td>\n

              		[latex]0 < X < 48[\/latex]<\/td>\n<\/td>\n<\/tr>\n
              <\/td>\n[latex]X \\leq 70[\/latex]<\/td>\nIf the speed is no more than 70 miles\u00a0 per hour (mph), it means that it can be\u00a0 anywhere from 0 mph up to and\u00a0 including 70 mph.<\/td>\n<\/tr>\n
              A temperature\u00a0 above 100.2 is\u00a0 considered a\u00a0 fever for<\/p>\n

              COVID-19.<\/td>\n

              		<\/td>\nIf a temperature above 100.2 is\u00a0 considered a fever for COVID-19, it\u00a0 means that it can be any value greater\u00a0 than 100.2. This value does not\u00a0 include 100.2.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
              \n

              Question 5<\/h3>\n

              Use probability notation to represent the following statements. Use [latex]X[\/latex] to represent the random variable.<\/p>\n

                \n
              1. The probability that the commute time will be less than 30 minutes<\/li>\n
              2. The probability that the temperature will be above 100.2\u00b0 F<\/li>\n
              3. A heart rate of at least 80 bpm<\/li>\n<\/ol>\n<\/div>\n
                \n

                Question 6<\/h3>\n

                You will need to be able to check criteria to determine whether or not a normal distribution can be used to approximate probabilities of a binomial distribution using the following inequalities: [latex]np > 10 \\mbox{ and } n(1 \u2013 p) > 10[\/latex].<\/p>\n

                  \n
                1. Suppose you know that [latex]n = 10 \\mbox{ and } p = 0.90[\/latex]. Is [latex]np > 10 \\mbox{ AND } n(1 \u2013 p)[\/latex]?<\/li>\n
                2. If [latex]n = 490 \\mbox{ and } p = 0.64[\/latex], are both [latex]np > 10 \\mbox{ and } n(1 \u2013 p) > 10[\/latex]?<\/li>\n<\/ol>\n<\/div>\n
                  \n

                  Question 7<\/h3>\n

                  In probability theory, a continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution. We do this by adjusting the discrete whole numbers in a binomial distribution so that any individual value, X, is represented in the normal distribution by the interval form:<\/p>\n

                  [latex]X - 0.5 \\mbox{ to } X + 0.5[\/latex]<\/p>\n

                    \n
                  1. If [latex]X = 158[\/latex] , find [latex]X \\pm 0.5[\/latex].<\/li>\n
                  2. Describe the interval from Part a using interval notation.<\/li>\n
                  3. Shade the area that represents the interval you created in Part B using the following number line.
                    \n\"\"<\/li>\n<\/ol>\n<\/div>\n
                    \n

                    Question 8<\/h3>\n

                    In In-Class Activity 8.C, you were introduced to finding the mean of a binomial distribution. The following formulas can be used to find the mean ([latex]\\mu[\/latex]) and standard deviation ([latex]\\sigma[\/latex]) of a binomial random variable:<\/p>\n

                    [latex]\\mu = np \\mbox{ and } \\sigma = \\sqrt{np(1-p)}[\/latex]<\/p>\n

                    Suppose [latex]n = 178 \\mbox{ and } p = 0.17[\/latex].<\/p>\n

                      \n
                    1. Find [latex]\\mu[\/latex]. Round your answer to the nearest whole number.<\/li>\n
                    2. Find [latex]\\sigma[\/latex]. Round your answer to the nearest whole number.<\/li>\n<\/ol>\n<\/div>\n

                       <\/p>\n

                      1. United States Census Bureau. (2021, July 9). American Community Survey Data<\/em>. https:\/\/www.census.gov\/programs-surveys\/acs\/data.html ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":16,"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-5150","chapter","type-chapter","status-publish","hentry"],"part":4997,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5150","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":9,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5150\/revisions"}],"predecessor-version":[{"id":5161,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5150\/revisions\/5161"}],"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\/5150\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5150"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5150"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5150"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}