Statistics Normal Distribution

[Junior1]

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.

 

[I like Serena]

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)

 

[HallsofIvy]

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?