Answer:
Anna's overall performance was better.
Step-by-step explanation:
Microeconomics:
Anna's Score = 85
Megan's Score = 76
Mean Score = 84
Standard deviation = 4
Macroeconomics:
Anna's Score = 85
Megan's Score = 95
Mean Score = 75
Standard deviation = 13
We will calculate the z-scores for both the students in both the subjects and then compare those values to see which student scored better overall. The z-score can be calculated by the formula:
z = (X -μ)/σ
where X = student's score
μ = mean score
σ = standard deviation
Anna's scores:
z(Micro) = (85-84)/4
=1/4
z(Micro) = 0.25
z(Macro) = (85-75)/13
= 10/13
z(Macro) = 0.769
Overall z-score = 0.25 + 0.769 = 1.019
Megan's scores:
z(Micro) = (76-84)/4
= -8/4
z(Micro) = -2
z(Macro) = (95-75)/13
= 20/13
z(Macro) = 1.54
Overall z-score = -2 + 1.54 = -0.46
Clearly, Anna performed better than Megan because the overall z-score for Megan is -0.46 which is much less than that of Anna (1.019). Megan's overall z-score is negative which means it lies below the mean while that of Anna lies above the mean test scores. So, we can conclude that Anna's overall performance was better.
