MHB Statistics Normal Distribution

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Eleanor scored 680 on the SAT math section, with a mean of 547 and a standard deviation of 85, resulting in a standardized score of 1.553 when calculated. Gerald scored 27 on the ACT, where the mean is 21.3 and the standard deviation is 3.4, yielding a standardized score of 1.676. Comparing their standardized scores indicates that Gerald performed better than Eleanor when assuming both tests measure the same ability. The discussion emphasizes the importance of standardized scores in evaluating performance across different assessments. Overall, Gerald's higher standardized score suggests he has the superior performance in this context.
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Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 547 and standard deviation 85.
Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and standard deviation 3.4.

What is Elanor's standardized score? ______ Round to 3 decimal places.
What is Gerald's standardized score?________ Round to 3 decimal places.
Assuming that both tests measure the same kind of ability, who has the higher score?
___Gerald.
___Elanor.
___They both did equally well.
 
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Junior said:
Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 547 and standard deviation 85.
Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and standard deviation 3.4.

What is Elanor's standardized score? ______ Round to 3 decimal places.
What is Gerald's standardized score?________ Round to 3 decimal places.
Assuming that both tests measure the same kind of ability, who has the higher score?
___Gerald.
___Elanor.
___They both did equally well.

Hi Junior! Welcome to MHB! ;)

A standardized score is calculated by taking the score, subtract the mean, and divide by the standard deviation.
What would we get as standardized scores? (Wondering)
 
Equivalently, the 'standard score' is the number of standard deviations the score is above or below the mean. Eleanor scored 680 and the mean is 547 so she scored 680- 547= 133 above the mean. If the standard deviation is 85, how many "standard deviations" is that?
 
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