On this semesters final exam, john scored 72 on his calculus exam and 53 on his statistics exam. The z score for both exams was the same. Which on would he do better on?

a. calculus
b.statistics
c. the exam scores are equivalent

I thought I answered this previously. If the Z scores are equal, he did equally well on both exams.

To determine which exam John did better on, we need to compare the z-scores for both exams. The z-score quantifies the number of standard deviations a data point is from the mean.

To calculate the z-score for each exam, we need the mean and standard deviation for each exam.

Let's assume the mean calculus score is μ1 and the standard deviation is σ1.
Similarly, the mean statistics score is μ2 and the standard deviation is σ2.

Since the z-scores are the same for both exams, we can write the equations:

(z-calculus) = (72 - μ1) / σ1 ------------ (1)
(z-statistics) = (53 - μ2) / σ2 ------------ (2)

Given that the z-scores are equal, we can set equation (1) equal to equation (2):

(72 - μ1) / σ1 = (53 - μ2) / σ2

To compare the two scores, we can rearrange the equation to solve for (72 - μ1) / σ1:

(72 - μ1) / σ1 = (53 - μ2) / σ2

Cross-multiply:

(72 - μ1) * σ2 = (53 - μ2) * σ1

Expand:

72σ2 - μ1σ2 = 53σ1 - μ2σ1

Rearrange the equation:

72σ2 - 53σ1 = μ1σ2 - μ2σ1

Now let's analyze the equation. Since μ1 and μ2 are means, the higher value will indicate a better performance. Therefore, the side with the higher value is the exam John did better on.

If (72σ2 - 53σ1) > 0, then John did better on the calculus exam (a).
If (72σ2 - 53σ1) < 0, then John did better on the statistics exam (b).
If (72σ2 - 53σ1) = 0, then both scores are equivalent (c).

To determine the final result, you will need the values of σ1 and σ2 (the standard deviations for calculus and statistics) to calculate (72σ2 - 53σ1).