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Suppose that 250 students take a test, of which 100 are sophomores, 140 are juniors and 110 are seniors. Let X be the random variable representing the score of each student on the test. Suppose that the sophomores have an average of 60 juniors have an average of 67 and the seniors have an average of 77. Find E(X) using conditioning. Use the appropriate notation to explain your answer.

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MechEngineer

Answer:

95.4

Step-by-step explanation:

The overall average score would be the total score divided by the total number of students. The total score is the sum of the product of the average of each student body and their average score

[tex]E(x) = \frac{E_1n_1 + E_2n_2+E_3n_3}{n_1+n_2+n_3}[/tex]

[tex]E(x) = \frac{100*60+140*67+110*77}{250} = \frac{23850}{250} = 95.4[/tex]

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