A metropolitan school system consists of threedistricts-north, south, and centra

Question

A metropolitan school system consists of threedistricts-north, south, and central. The north districtcontains 25% of all students, the south district contains 40%, andthe central district contains 35%. A minimum -competency testwas given to all students; 10% of the north district studentsfailed, 15% of the south district students failed, and 5% of thecentral district students failed. a. Develop a probability tree showing all marginal,conditional, and joint probabilities. b. Develop a joint probability table. c. What is the probability that a student selected atrandom failed the test? A metropolitan school system consists of threedistricts-north, south, and central. The north districtcontains 25% of all students, the south district contains 40%, andthe central district contains 35%. A minimum -competency testwas given to all students; 10% of the north district studentsfailed, 15% of the south district students failed, and 5% of thecentral district students failed. a. Develop a probability tree showing all marginal,conditional, and joint probabilities. b. Develop a joint probability table. c. What is the probability that a student selected atrandom failed the test?

Explanation / Answer

a)                  _____ Pass (0.9) = 0.225                  / North (0.25) ----- Fail (0.1) = 0.025                  ______Pass (0.85) = 0.34                /     South (0.4)---------Fail (0.15) = 0.06        ____Pass (0.95) = 0.3325                                  / Central (0.35)------Fail (0.05) = 0.0175 Where the numbers in the brackets are the marginal or conditionalprobabilities, and the numbers after the equal signs are the jointprobabilities. b) Pass Fail Total North 0.9x0.25 = 0.225 0.1x0.25 = 0.025 0.25 South 0.85x0.4 = 0.34 0.15x0.4 = 0.06 0.4 Central 0.95x0.35 = 0.3325 0.05x0.35 = 0.0175 0.35 Total 0.8975 0.1025 1 c) From the table, the probability that a randomly chosen studentfailed the test is 0.1025.

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