{"id":236,"date":"2023-01-17T19:27:39","date_gmt":"2023-01-18T00:27:39","guid":{"rendered":"https:\/\/opentextbc.ca\/busstatsancillary\/?post_type=chapter&p=236"},"modified":"2023-01-20T13:54:17","modified_gmt":"2023-01-20T18:54:17","slug":"hypergeometric-distribution","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/busstatsancillary\/chapter\/hypergeometric-distribution\/","title":{"raw":"4.1 Hypergeometric Distribution","rendered":"4.1 Hypergeometric Distribution"},"content":{"raw":"The following activities and questions relate to material covered in Chapter 4.1<\/a><\/span>\u00a0<\/span>Hypergeometric Distribution<\/span><\/a>\u00a0in\u00a0Introductory Business Statistics (OpenStax)<\/em><\/a>.\r\n
Data sets for the following questions are available in Excel: 4.1 Data Sets [XLSX]<\/a>.<\/div>\r\n

Questions<\/h1>\r\n
    \r\n \t
  1. A member of the YT Elites Volleyball Club has a volleyball practice four days a week. She practices for all of the four days 87% of the time, three days 6% of the time, two days 4% of the time, one day 2% of the time, and no days 1% of the time. Suppose one week is randomly selected.\r\n
      \r\n \t
    1. Define the random variable X.<\/li>\r\n \t
    2. Construct a probability distribution table for the data.<\/li>\r\n \t
    3. We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    4. Valerie volunteers at the local territorial farmer\u2019s market no more than 7 hours and no less than 1 hour, per week. She volunteers 7 hours 42% of this summer, 6 hours 29% of this summer, 5 hours 10% of this summer, 4 hours 7% of this summer, 3 hours 6% of this summer, 2 hours 4% of this summer, and 1 hour 2% of this summer.\r\n
        \r\n \t
      1. Define the random variable X.<\/li>\r\n \t
      2. What values does X take on?<\/li>\r\n \t
      3. Construct a table to organize the data.<\/li>\r\n \t
      4. Find the probability that Valerie volunteers for more than 5 hours, per week.<\/li>\r\n \t
      5. Find the probability that Valerie volunteers for at most 3 hours, per week.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
      6. Over the last 13 years, Yukon University, has averaged 5,574 students enrolled, per year. Of these enrollments 11.35% are full-time credit students, 10.15% are part-time credit students, and 78.49% are non-credit students. One student is selected at random. Data source: Yukon University. Fast facts, Credit program enrolment<\/em>. (2021). https:\/\/www.yukonu.ca\/about-us\/publications-plans-reports\/institutional-research\/fast-facts\r\n
          \r\n \t
        1. Define the Random Variable, is it discrete or continuous?<\/li>\r\n \t
        2. Use the data to construct a probability distribution table.<\/li>\r\n \t
        3. What is the probability that the student will be enrolled in credit courses?<\/li>\r\n \t
        4. What are the two characteristics required for a probability distribution function to be discrete?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

          Solutions<\/h1>\r\n
            \r\n \t
          1. \r\n
              \r\n \t
            1. Let x be the number of days volleyball member attends the practice per week.<\/li>\r\n \t
            2. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
              x<\/th>\r\nP(x)<\/th>\r\n<\/tr>\r\n
              0<\/td>\r\n0.01<\/td>\r\n<\/tr>\r\n
              1<\/td>\r\n0.02<\/td>\r\n<\/tr>\r\n
              2<\/td>\r\n0.04<\/td>\r\n<\/tr>\r\n
              3<\/td>\r\n0.06<\/td>\r\n<\/tr>\r\n
              4<\/td>\r\n0.87<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
            3. Each probability is between zero (0) and one (1), inclusive.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
            4. \r\n
                \r\n \t
              1. Let X = the number of hours Valerie volunteers at the market.<\/li>\r\n \t
              2. The values that X takes on are the number of hours Valerie volunteers at the market. X = 1, 2, 3, 4, 5, 6, 7<\/li>\r\n \t
              3. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                X<\/th>\r\nP(X) (%)<\/th>\r\n<\/tr>\r\n
                1<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
                2<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
                3<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
                4<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
                5<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
                6<\/td>\r\n29<\/td>\r\n<\/tr>\r\n
                7<\/td>\r\n42<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
              4. P(X > 5) = 29% + 42% = 71%.\r\nThe probability that Valerie volunteers for more than 5 hours per week is 71%.<\/li>\r\n \t
              5. P(X < 3) = 2% + 4% + 6% = 12%.\r\nThe probability that Valerie volunteers for at most 3 hours per week is 12%.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
              6. \r\n
                  \r\n \t
                1. The discrete random variable is the type of program the student is enrolled in. (FT, PT, NC)<\/li>\r\n \t
                2. \r\n\r\n\r\n\r\n\r\n\r\n\r\n
                  X<\/th>\r\nP(X)<\/th>\r\n<\/tr>\r\n
                  Full-time<\/td>\r\n0.1135<\/td>\r\n<\/tr>\r\n
                  Part-time<\/td>\r\n0.1015<\/td>\r\n<\/tr>\r\n
                  Non-credit<\/td>\r\n0.7849<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
                3. There is a 11.35% + 10.15% = 21.51% chance the randomly selected student will be enrolled in credit courses.<\/li>\r\n \t
                4. Each probability is between 0 and 1, inclusive. The sum of probabilities is 1.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"

                  The following activities and questions relate to material covered in Chapter 4.1<\/a><\/span>\u00a0<\/span>Hypergeometric Distribution<\/span><\/a>\u00a0in\u00a0Introductory Business Statistics (OpenStax)<\/em><\/a>.<\/p>\n

                  Data sets for the following questions are available in Excel: 4.1 Data Sets [XLSX]<\/a>.<\/div>\n

                  Questions<\/h1>\n
                    \n
                  1. A member of the YT Elites Volleyball Club has a volleyball practice four days a week. She practices for all of the four days 87% of the time, three days 6% of the time, two days 4% of the time, one day 2% of the time, and no days 1% of the time. Suppose one week is randomly selected.\n
                      \n
                    1. Define the random variable X.<\/li>\n
                    2. Construct a probability distribution table for the data.<\/li>\n
                    3. We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?<\/li>\n<\/ol>\n<\/li>\n
                    4. Valerie volunteers at the local territorial farmer\u2019s market no more than 7 hours and no less than 1 hour, per week. She volunteers 7 hours 42% of this summer, 6 hours 29% of this summer, 5 hours 10% of this summer, 4 hours 7% of this summer, 3 hours 6% of this summer, 2 hours 4% of this summer, and 1 hour 2% of this summer.\n
                        \n
                      1. Define the random variable X.<\/li>\n
                      2. What values does X take on?<\/li>\n
                      3. Construct a table to organize the data.<\/li>\n
                      4. Find the probability that Valerie volunteers for more than 5 hours, per week.<\/li>\n
                      5. Find the probability that Valerie volunteers for at most 3 hours, per week.<\/li>\n<\/ol>\n<\/li>\n
                      6. Over the last 13 years, Yukon University, has averaged 5,574 students enrolled, per year. Of these enrollments 11.35% are full-time credit students, 10.15% are part-time credit students, and 78.49% are non-credit students. One student is selected at random. Data source: Yukon University. Fast facts, Credit program enrolment<\/em>. (2021). https:\/\/www.yukonu.ca\/about-us\/publications-plans-reports\/institutional-research\/fast-facts\n
                          \n
                        1. Define the Random Variable, is it discrete or continuous?<\/li>\n
                        2. Use the data to construct a probability distribution table.<\/li>\n
                        3. What is the probability that the student will be enrolled in credit courses?<\/li>\n
                        4. What are the two characteristics required for a probability distribution function to be discrete?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                          Solutions<\/h1>\n
                            \n
                          1. \n
                              \n
                            1. Let x be the number of days volleyball member attends the practice per week.<\/li>\n
                            2. \n\n\n\n\n\n\n\n\n
                              x<\/th>\nP(x)<\/th>\n<\/tr>\n
                              0<\/td>\n0.01<\/td>\n<\/tr>\n
                              1<\/td>\n0.02<\/td>\n<\/tr>\n
                              2<\/td>\n0.04<\/td>\n<\/tr>\n
                              3<\/td>\n0.06<\/td>\n<\/tr>\n
                              4<\/td>\n0.87<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                            3. Each probability is between zero (0) and one (1), inclusive.<\/li>\n<\/ol>\n<\/li>\n
                            4. \n
                                \n
                              1. Let X = the number of hours Valerie volunteers at the market.<\/li>\n
                              2. The values that X takes on are the number of hours Valerie volunteers at the market. X = 1, 2, 3, 4, 5, 6, 7<\/li>\n
                              3. \n\n\n\n\n\n\n\n\n\n\n
                                X<\/th>\nP(X) (%)<\/th>\n<\/tr>\n
                                1<\/td>\n2<\/td>\n<\/tr>\n
                                2<\/td>\n4<\/td>\n<\/tr>\n
                                3<\/td>\n6<\/td>\n<\/tr>\n
                                4<\/td>\n7<\/td>\n<\/tr>\n
                                5<\/td>\n10<\/td>\n<\/tr>\n
                                6<\/td>\n29<\/td>\n<\/tr>\n
                                7<\/td>\n42<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                              4. P(X > 5) = 29% + 42% = 71%.
                                \nThe probability that Valerie volunteers for more than 5 hours per week is 71%.<\/li>\n
                              5. P(X < 3) = 2% + 4% + 6% = 12%.
                                \nThe probability that Valerie volunteers for at most 3 hours per week is 12%.<\/li>\n<\/ol>\n<\/li>\n
                              6. \n
                                  \n
                                1. The discrete random variable is the type of program the student is enrolled in. (FT, PT, NC)<\/li>\n
                                2. \n\n\n\n\n\n\n
                                  X<\/th>\nP(X)<\/th>\n<\/tr>\n
                                  Full-time<\/td>\n0.1135<\/td>\n<\/tr>\n
                                  Part-time<\/td>\n0.1015<\/td>\n<\/tr>\n
                                  Non-credit<\/td>\n0.7849<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
                                3. There is a 11.35% + 10.15% = 21.51% chance the randomly selected student will be enrolled in credit courses.<\/li>\n
                                4. Each probability is between 0 and 1, inclusive. The sum of probabilities is 1.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"author":123,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-236","chapter","type-chapter","status-publish","hentry"],"part":71,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/236","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":4,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/236\/revisions"}],"predecessor-version":[{"id":329,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/236\/revisions\/329"}],"part":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/parts\/71"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/236\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/media?parent=236"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapter-type?post=236"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/contributor?post=236"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/license?post=236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}