In this case, we will use the z-score to compare each student to the distribution corresponding to each career.
a) Evan took a test in Art History and he earned a 74.1.
The scores in Art History have a mean of 70.6 and a standard deviation of 8.9.
We can then calculate the corresponding z-score for this result as:
[tex]z=\frac{X-\mu}{\sigma}=\frac{74.1-70.6}{8.9}=\frac{3.5}{8.9}\approx0.3933[/tex]b) Jeff took a test in Social Studies and earned a 62.7.
The scores in Social Studies have a mean of 62.5 and a standard deviation of 9.5.
Then, we can calculate the z-score as:
[tex]z=\frac{X-\mu}{\sigma}=\frac{62.7-62.5}{9.5}=\frac{0.2}{9.5}\approx0.021[/tex]