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Question 599:



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This question requires the use of standard scores or "z-scores." We need to convert Jose's raw score of 545 to a standard score by subtracting it from the mean and dividing that result by the standard deviation. This gets us (545-1026)/209 = a z-score of -2.3014. Notice the negative sign. When you have a negative z-score, you know the score is below the mean.


To find the equivalent ACT score we need to find what raw score is 2.3014 standard deviations below the mean. To do so, we setup a simple equation and solve.


  1. (x-20.8)/4.8 = -2.3014
  2. x-20.8 = -11.0469
  3. x = 9.753


To double-check our math we can find the z-score for 9.753 on the ACT: (9.753-20.8)/4.8 = -2.3014.


So a score on the SAT of a 545 gets us an equivalent score of 9.753 on the ACT as these both have normal scores of -2.3014.

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