Question

college and university debt a student graduated from a 4 - year college with an outstanding loan of $9733, where the average debt is $8594 with a standard deviation of $1839. another student graduated from a university with an outstanding loan of $12,228, where the average of the outstanding loans was $10,313 with a standard deviation of $2186. part: 0 / 2 part 1 of 2 find the corresponding z - score for each student. round z - scores to two decimal places. college student: z = university student: z =

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for college student

For the college student, $x = 9733$, $\mu=8594$, and $\sigma = 1839$.
$z_1=\frac{9733 - 8594}{1839}=\frac{1139}{1839}\approx0.62$

Step3: Calculate z - score for university student

For the university student, $x = 12228$, $\mu = 10313$, and $\sigma=2186$.
$z_2=\frac{12228 - 10313}{2186}=\frac{1915}{2186}\approx0.88$

Answer:

College student: $z = 0.62$
University student: $z = 0.88$