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​Anna, a business​ major, took final exams in both Microeconomics and Macroeconomics and scored 85 on both. Her roommate​ Megan, also taking both​ courses, scored 76 on the Micro exam and 95 on the Macro exam.​ Overall, student scores on the Micro exam had a mean of 84 and a standard deviation of 4​, and the Macro scores had a mean of 75 and a standard deviation of 13. Which​ student's overall performance was​ better? Explain.

Respuesta :

salwanadeem

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.

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