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

Z = (X - mean)/S.D

For Eleanor

Z = (680 - 555)/79

Z = 125/79 = 1.58

For Gerald

Z = (27.0 - 21.9)/3.3

Z = 5.1/3.3 = 1.55

They both did equally. Because Eleanor and Gerald test scores are approximately 2 S.D above the mean. From empirical rule, they both have 95% test scores.