Statistics Normal Distribution

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SUMMARY

Eleanor scored 680 on the SAT mathematics section, which has a Normal distribution with a mean of 547 and a standard deviation of 85. Her standardized score is calculated as (680 - 547) / 85, resulting in a standardized score of 1.565. Gerald scored 27 on the ACT mathematics test, which has a Normal distribution with a mean of 21.3 and a standard deviation of 3.4. His standardized score is (27 - 21.3) / 3.4, yielding a standardized score of 1.676. Therefore, Gerald has the higher standardized score.

PREREQUISITES
  • Understanding of Normal distribution and its properties
  • Knowledge of standardized score calculation methods
  • Familiarity with SAT and ACT scoring systems
  • Basic statistical concepts such as mean and standard deviation
NEXT STEPS
  • Learn how to calculate standardized scores for different distributions
  • Explore the implications of Normal distribution in educational assessments
  • Study the differences between SAT and ACT scoring methodologies
  • Investigate the use of z-scores in statistical analysis
USEFUL FOR

Students preparing for standardized tests, educators analyzing test scores, and statisticians interested in educational assessment metrics.

Junior1
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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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