5. Suppose that a hypothetical university draws its entering students from three

Question

5. Suppose that a hypothetical university draws its entering students from three regions. 40% of students are from region A, 35% are from region B, and 25% are from region C. Of the region A students who enter as freshmen, 80% eventually graduate. Of the region B students who enter as freshmen, 70% eventually graduate. of the region C students who enter as freshmen, 90% eventually graduate. Using the table below to show your work, answer the following questions. Round your answers to three decimal places. (8 pts.) a. What percent of the university's entering freshmen eventually graduate? b. If a student graduates from the university, what is the probability the student is from (4 pts.) i. region A? (4 pts.) ii. region B? (4 pts.) ii. region C? Workspace Region

Explanation / Answer

5)a) The percentage of the university's entering freshmen eventually graduate = (0.8 * 0.4 + 0.7 * 0.35 + 0.9 * 0.25) * 100 = 79%

b)i) P(from region A | graduates from the university) = P(graduates from the university | from region A) * P(from region A)/P(graduates from the university)

= 0.8 * 0.4/0.79 = 0.405

ii) P(from region B | graduates from the university) = P(graduates from the university | from region B) * P(from region B)/P(graduates from the university)

= 0.7 * 0.35/0.79 = 0.310

iii) P(from region C | graduates from the university) = P(graduates from the university | from region C) * P(from region C)/P(graduates from the university)

= 0.9 * 0.25/0.79 = 0.285

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