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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 12%12\% are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?

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Q. High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 12%12\% are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
  1. Question Prompt: question_prompt: How many standard deviations above the mean does a student need to score to be in the top 12%12\%?
  2. Find Cumulative Area: In a normal distribution, the top 12%12\% corresponds to the area to the right under the curve. We need to find the zz-score that corresponds to the cumulative area of 0.880.88 (since 100%−12%=88%100\% - 12\% = 88\%).
  3. Use Z-Table or Calculator: We can use a z-table or a calculator to find the z-score that corresponds to the cumulative area of 0.880.88. Looking at the z-table, we find that the z-score is approximately 1.1751.175.

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