Question

An incoming MBA student took placement exams in economics and mathematics. In​ economics, she scored 80 and in math 86. The overall results on the economics exam had a mean of 73 and a standard deviation of 10​, while the mean math score was 67​, with a standard deviation of 12. On which exam did she do better compared with the other​ students? Since she scored (nothing) standard deviations ▼ ( below or above) the mean in economics and (nothing) standard deviations ▼ (below or above) the mean in​ mathematics, she did better on the ▼ (economics or mathematics) exam. ​(Round to two decimal places as​ needed.)

Answer 1

To find out in which exam the student did better, we find the z-score for each of the exams. The z-scores also tell us how many standard deviations above/below the mean the scores are:

For Economics:

                                   

For Mathematics:

                                   

Since the z-score for mathematics is higher than economics, we conclude that she did better in mathematics than economics.

Now we also know the answers to the fill in the blanks:

Since she scored 0.7 standard deviations above the mean in economics and 1.58 standard deviations above the mean in mathematics, she did better on the mathematics exam.