{"id":"cb_question_bank:4aed34b8-3b40-48f7-b587-2b080f0ad2d4","source_id":"cb_question_bank","source_item_id":"4aed34b8-3b40-48f7-b587-2b080f0ad2d4","external_id":null,"ibn":"01550-DC","question_id":"e7d9649f","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.F.","skill":"Inference from sample statistics and margin of error","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A random sample of 50 people from a town with a population of 14,878 were asked to name their favorite flavor of ice cream. If 7 people in the sample named chocolate as their favorite ice‑cream flavor, about how many people in the town would be expected to name chocolate?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A random sample of 50&nbsp;people from a town with a population of&nbsp;14,878 were asked to name their favorite flavor of ice&nbsp;cream. If 7&nbsp;people in the sample named chocolate as their favorite ice‑cream flavor, about how many people in the town would be expected to name chocolate?</p>\n","rationale_html":"<p>Choice B is correct. Let <span class=\"italic\">x </span>be the number of people in the entire town that would be expected to name chocolate. Since the sample of 50 people was selected at random, it is reasonable to expect that the proportion of people who named chocolate as their favorite ice-cream flavor would be the same for both the sample and the town population. Symbolically, this can be expressed as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92d70538302db14a2012390decab564d00ebefa537bac0bedac1f9fd5e718194\" alt=\"the fraction 7 over 50, end fraction, equals, the fraction x over 14,878\"></span>. Using cross multiplication,&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/422ef7f465460060a196e037259112cdbb203c2b2daf3e914bd0fbe3267cdf0d\" alt=\"7 times 14,878 equals, x times 50\"></span>; solving for <span class=\"italic\">x</span> yields 2,083. The choice closest to the value of 2,083 is choice B, 2,100.</p><p>Choices A, C, and D are incorrect and may be the result of errors when setting up the proportion, solving for the unknown, or incorrectly comparing the choices to the number of people expected to name chocolate, 2,083.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.614000+00:00","source_updated_at":"2023-08-02T20:25:59.614000+00:00","options":[{"label":"A","content_html":"<span class=\"align align-44\">350</span>\n","ord":0},{"label":"B","content_html":"<span class=\"align align-44\">2,100</span>\n","ord":1},{"label":"C","content_html":"<span class=\"align align-44\">7,500</span>\n","ord":2},{"label":"D","content_html":"<span class=\"align align-44\">10,500</span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}