High School

If the average IQ score for 10-year-olds is 115 with a standard deviation of 20, what is the raw score one would need to be in the top 25 percent of all individuals?

Answer :

Final answer:

To be in the top 75 percent of all individuals based on IQ scores, a raw score of approximately 128.48 would be needed.

Explanation:

To be in the top 75 percent of all individuals, you would need a score higher than 75 percent of the population. In this case, we can use the normal distribution and the concept of z-scores to find the corresponding IQ score. The z-score formula is given by z = (x - µ) / σ, where x is the raw score, µ is the mean, and σ is the standard deviation.




  3. First, find the z-score that corresponds to the 75th percentile using the invNorm function: invNorm(0.75) = 0.674

  6. Plug in the values into the z-score formula: 0.674 = (x - 115) / 20

  9. Solve for x: x = (0.674 * 20) + 115 = 128.48



Therefore, a raw score of approximately 128.48 would be needed to be in the top 75 percent of all individuals.

Learn more about IQ scores here:

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