Question

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 535 and standard deviation 97.

Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 22.8 and standard deviation 2.1.

1. What is Elanor's standardized score?
   
   Round to 2 decimal places.
   
2. What is Gerald's standardized score?
   
   Round to 2 decimal places.
   
3. Assuming that both tests measure the same kind of ability, who has the higher score?
   
   • Gerald.
   • Elanor.
   • They both did equally well.

Answer 1

Let the standardized score of Elanor be ZE .

where is the mean score in Elanor's test and be the standard deviation of the scores in Elanor's test.

Let the standardized score of Gerald be ZG .

where is the mean score in Gerald's test and be the standard deviation of the scores in Gerald's test.

Assuming that both tests measure the same kind of ability,

Hence Gerald's score is higher Elanor's score.

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