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The government decides to base a lump-sum tax on the score on a 10 question test used to determine ability

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The government decides to base a lump-sum tax on the score on a 10 question test used to determine ability. Assume everyone who takes the test knows which questions they answer correctly and which they answer incorrectly. What will be the mean score on the test if the lump-sum tax is an increasing function of the score?