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Anna, a business​ major, took final exams in both Microeconomics and Macroeconomics and scored 81 on...

Anna, a business​ major, took final exams in both Microeconomics and Macroeconomics and scored 81 on both. Her roommate​ Megan, also taking both​ courses, scored 79 on the Micro exam and 86 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 71 and a standard deviation of 16. Which​ student's overall performance was​ better? Explain.

Math   Statistics-And-Probability   
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Answer #1

Mean score for Micro exam is 84 with a standard deviation of 4

Mean score for Macro exam is 71 with a standard deviation of 16

Anna score for Micro and Macro exams is 81 on both.

Megan score for Micro is 79 and for macro is 86

It is clear from the data that Anna score for micro is within 1 standard deviation of overall student scores and for macro is also within 1 standard deviation of overall student scores.

Megan score for micro is outside 1 standard deviation of overall student scores and for macro is within 1 standard deviation of overall student scores.

So, it is clear that Megan score are more spreaded as compared to Anna. Anna performance was better than Megan because Anna scores are within 1 standard deviation whereas Megan scores are not all inside 1 standard deviation.

Thus, Anna performance was better than Megan

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