Tree Diagrams_WS university.pdf

Students with sats under 1400 are rejected those who

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• Students with SAT’s under 1400 are rejected. • Those who are still considered will have their GPA examined. Those with GPA’s 3.7 and above are accepted. Those under 3.2 are rejected. • Those with GPA’s between 3.2 and below 3.7 will have their essays read by 4 admission officers. If 3 out of 4 officers like the essay, then the student is admitted. If not, the student is rejected. Over the years, the following statistics have been compiled: • On the average, 57% of students who apply to that university have SAT’s 1400 or over. • Of the students with SAT’s 1400 and over... • 58% have GPA’s 3.7 or above • 31% have GPA’s between 3.2 and 3.7 • Of the students who have their essays read, there is a 50% chance that an admission officer will like their essay Make a tree diagram for this problem and then answer the following questions. SAT over 1400 - .57 SAT under 1400 - .43 GPA>3.7 - .58 Accept = .3306 GPA < .32 - .11 Reject - .0627 3.2<GPA<3.7 - .31 Like essay - .3125 Don’t like essay - .6875 Accept - .0552 Reject - .1215 Reject - .43 Find the probabilities that a. a student is accepted - .3858 b. a student is rejected - .6142 c. if a student is accepted, he had a GPA of d. if a student is accepted, he got in 3.7 or above - .3306 .3858 = .8569 because of writing good essays - .0552 .3858 = .1431 e. If a student is rejected, it’s because his f. If a student has SAT’s over 1400, he is accepted essays .1215 .6142 = .1978 .3858 .57 = .6768
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