Two language majors, Anna and Megan, took exams in two languages. Anna scored 81

Question

Two language majors, Anna and Megan, took exams in two languages. Anna scored 81 on both exams. Megan scored 73 on the first exam and 90 on the second exam. Overall, student scores on the first exam had a mean of 85 and a standard deviation of 3, and the second exam scores had a mean of 73 and a standard deviation of 13. a) To qualify for language honors, a major must maintain at least an 85 average across all language courses taken. So far, which of Anna and Megan quality? b) Which students overall performance was better? a) Which of Anna and Megan qualify for language honors? A. Only Anna qualifies B. Neither Anna nor Megan quality C. Both Anna and Megan quality D. Only Megan qualifies b) performed better overall.

Explanation / Answer

a)
Average score of Anna = (81+81)/2 = 81
Average score of Megan = (73+90)/2 = 81.5
As average score of Anna and Megan is below the qualifying score of 85
Neither Anna nor Megan qualify

b)
z-score of Anna on 1st examination = (81-85)/3 = -1.33
z-score of Megan on 1st examination = (73-85)/3 = -4
z-score of Anna on 2nd examination = (81-73)/13 = 0.61
z-score of Anna on 2nd examination = (90-73)/13 = 1.31
Sum of z-score of Anna = -1.33 + 0.61 = -0.72
Sum of z-score of Megan = -4 + 1.31 = -2.69

As the z-score of Anna > z-score of Megan, Anna performed better overall

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