Question

Evan and Jeff began arguing about who did better on their tests, but they couldn't decide who did better giventhat they took different tests. Evan took a test in Art History and earned a 74.1, and Jeff took a test in SocialStudies and earned a 62.7. Use the fact that all the students' test grades in the Art History class had a mean of70.6 and a standard deviation of 8.9, and all the students' test grades in Social Studies had a mean of 62.5 anda standard deviation of 9.5 to answer the following questions.a) Calculate the z-score for Evan's test grade.Z=b) Calculate the z-score for Jeff's test grade.Z=Which

Answer 1

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:

`z=(X-\mu)/(\sigma)=(74.1-70.6)/(8.9)=(3.5)/(8.9)\approx0.3933`

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:

`z=(X-\mu)/(\sigma)=(62.7-62.5)/(9.5)=(0.2)/(9.5)\approx0.021`