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East and west districts

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The metropolitan school system consists of two districts, east and west. The east district contains 35% of all students, and the west district contains the other 65%. A vocational aptitude test was given to all students; 10% of the east district students failed, and 25% of the west district students failed. Given that a students failed, and 25% of the west district students failed. Given that a student failed the test, what is the posterior probability that the student came from east district?

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Solution Preview

- of students in east = 35%
- of students failing in east = 10%
- of students in west = 65%
- ...

Solution Summary

This solution provides calculations for posterior probability.

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Brooks City has three consolidated high schools, each with a capacity of 1,200 students.

Brooks City has three consolidated high schools, each with a capacity of 1,200 students. The school board has partitioned the city into five busing districts - north, south, east, west, and central - each with different high school student populations. the three schools are located in the central, west, and south districts. Some students must be bused outside of theri district, and the school board wants to minimize the total bus distance traveled by these students. The average distances from each district to the three schools and the total student population in each district are as follows.
Distance (miles)
Central West South Student
District School School School Population

North 8 11 14 700
South 12 9 0 300
East 9 16 10 900
West 8 0 9 600
Central 0 8 12 500

The school board wants to determine the number of students to bus from each district to each school to minimize the total busing miles traveled:
A. Formulate a linear programming model for this problem.
B. Solve the model using the computer. QM for Windows Preferred.

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