Correction
On this semesters final exam, john scored 72 on his calculus exam, (class distribution (u=65, \?=3.57)\)
) and 53 on his statistics exam (class distribution :u=49, ?=2.04. Which exam should he get the better grade.
z1=72-65/3.57=1.960
Z2=53-49/2.04=1.960
From your data, he did equally well on both exams.
To determine which exam John scored better on, we need to compare the Z-scores for both exams. Z-scores allow us to compare scores from different distributions.
The formula to calculate the Z-score is:
Z = (X - μ) / σ
Where:
X = actual score
μ = mean of the distribution
σ = standard deviation of the distribution
For John's calculus exam:
X1 = 72 (actual score)
μ1 = 65 (mean of the calculus distribution)
σ1 = 3.57 (standard deviation of the calculus distribution)
Plugging in the values into the Z-score formula:
Z1 = (72 - 65) / 3.57
Z1 = 1.960
For John's statistics exam:
X2 = 53 (actual score)
μ2 = 49 (mean of the statistics distribution)
σ2 = 2.04 (standard deviation of the statistics distribution)
Plugging in the values into the Z-score formula:
Z2 = (53 - 49) / 2.04
Z2 = 1.960
Both Z1 and Z2 have the same value of 1.960. This means that John's scores on both exams are equally good when compared to their respective class distributions. Therefore, he performed equally well on both exams.