stats question

Question

the average grade on an algebra exam was 76% with a standard deviation of 6 percentagepoints. the average grade on a chem exam was 81% with a standard deviation of 2 percentage points. julie got a grade of 83% on both exams. which exam did she do relatively better on? show all work

Answer 1

To answer this question, we will calculate Julie's Z-score for both exams.

 

Z-score for Algebra:

Mean, μ=76

St. Deviation, σ=6

 

Z (algebra)

= (x - μ) / σ

= (83 - 76) / 6

= 1.167

 

Z-score for Chemistry:

Mean, μ=81
St. Deviation, σ=2

 

Z (chemistry)
= (83 - 81) / 3
= 0.667

 

Since Z(algebra) = 1.167 > 0.667 = Z(chemistry), Julie scored higher relative to the mean on her algebra test. Therefore, Julie did relatively better on her Algebra test.