(Answered) A philosophy professor assigns letter grades on a test

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A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 63% C: Scores below the top 37% and above the bottom 22% D: Scores below the top 78% and above the bottom 7% F: Bottom 7% of scores. Scores on the test are normally distributed with a mean of 72 and a standard deviation of 8.1. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

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