Normally distributed

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 555 and standard deviation 79.

Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.9 and standard deviation 3.3.

What is Elanor's standardized score?


Round to 2 decimal places.

What is Gerald's standardized score?


Round to 2 decimal places.

Assuming that both tests measure the same kind of ability, who has the higher score?

Gerald.
Elanor.
They both did equally well.

Answer 1

Hi Alyssa,

This statistics question involves a formula, called the z-score, which is basically a standardized score for the number of standard deviations away from the mean a data point is.

The z-score formula is z= (x-u)/s

where z is the standardized score, x is the data point you are measuring, u is the mean, and s is the standard deviation.

For Eleanor, that would be z= (680-555)/79, which is ~1.58.

For Gerald, that would be z=(27-21.9)/3.3, which is ~1.55

Eleanor is further away from the mean on the positive end of the normal curve than Gerald, so Eleanor has the higher score.