According to the College Board, the SAT ERW \( \mu=497 \) and \( \sigma=115 \), and the Math \( \mu=513 \) and \( \sigma=120 \). Ted's ERW score was 730 , and his Math score was 760 . Were Ted's scores considered unusual scores?

To determine whether Ted's scores are considered unusual, we can calculate the z-scores for both his Evidence-Based Reading and Writing (ERW) score and his Math score. A z-score indicates how many standard deviations an individual score is from the mean. Typically, a z-score greater than 2 or less than -2 is considered unusual. The formula for calculating a z-score is: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the individual score, - \( \mu \) is the mean, - \( \sigma \) is the standard deviation. ### For the ERW score: - \( X = 730 \) - \( \mu = 497 \) - \( \sigma = 115 \) Calculating the z-score for the ERW score: \[ z_{ERW} = \frac{(730 - 497)}{115} = \frac{233}{115} \approx 2.03 \] ### For the Math score: - \( X = 760 \) - \( \mu = 513 \) - \( \sigma = 120 \) Calculating the z-score for the Math score: \[ z_{Math} = \frac{(760 - 513)}{120} = \frac{247}{120} \approx 2.06 \] ### Conclusion: - The z-score for Ted's ERW score is approximately \( 2.03 \). - The z-score for Ted's Math score is approximately \( 2.06 \). Both z-scores are greater than 2, which indicates that both of Ted's scores are considered unusual.