On this semesters final exam, john scored 72 on his calculus exam, (class distribution (u=65, \σ=3.57)\)
) and 53 on his statistics exam (class distribution :u=49, σ=2.04. Which exam should he get the better grade.
z1=72-65/3.57=1.960
Z2=53-49/3.57=1.120
To determine which exam John got the better grade in, we need to compare the z-scores for both exams. The z-score formula is given by:
z = (x - u) / σ
Where:
- x is John's score
- u is the mean of the class distribution
- σ is the standard deviation of the class distribution
Let's calculate the z-scores for both exams:
For calculus:
z1 = (72 - 65) / 3.57
= 1.96
For statistics:
z2 = (53 - 49) / 2.04
= 1.96
Now, we compare the z-scores. Since both z1 and z2 have the same value of 1.96, it means that John's score of 72 in calculus is the same as his score of 53 in statistics relative to their respective class distributions.
Therefore, John did equally well in both exams, based on the z-scores.