Problem

Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Danny scores two standard deviations below the mean, what percentile is he?

Solution

Step 1 :Assume that 500,000 people take the GED exam each year and their scores form a normal distribution. If Danny scores two standard deviations below the mean, we need to find the corresponding percentile.

Step 2 :Since Danny's score is two standard deviations below the mean, we can use the z-score table or a calculator to find the corresponding percentile. The z-score is -2.

Step 3 :Using the z-score table or a calculator, we find that the percentile corresponding to a z-score of -2 is approximately 2.28.

Step 4 :\(\boxed{\text{Final Answer: Danny is in the 2.28th percentile.}}\)

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