Questions: College and University Debt A student graduated from a 4-year college with an outstanding loan of 9832, where the average debt is 8427 with a standard deviation of 1858. Another student graduated from a university with an outstanding loan of 12,405, where the average of the outstanding loans was 10,381 with a standard deviation of 2117. 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=

College and University Debt A student graduated from a 4-year college with an outstanding loan of 9832, where the average debt is 8427 with a standard deviation of 1858. Another student graduated from a university with an outstanding loan of 12,405, where the average of the outstanding loans was 10,381 with a standard deviation of 2117. 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=
Transcript text: College and University Debt A student graduated from a 4-year college with an outstanding loan of $\$ 9832$, where the average debt is $\$ 8427$ with a standard deviation of $\$ 1858$. Another student graduated from a university with an outstanding loan of $\$ 12,405$, where the average of the outstanding loans was $\$ 10,381$ with a standard deviation of $\$ 2117$. Part: $0 / 2$ Part 1 of 2 Find the corresponding $z$ score for each student. Round $z$ scores to two decimal places. College student: $\quad z=$ $\square$ University student: $z=$ $\square$
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Solution

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Solution Steps

Step 1: Calculate the Difference

To find the $z$ score for the value $X=9832$ in the distribution, we first calculate the difference from the mean ($\mu=8427$). \[ X - \mu = 9832 - 8427 = 1405 \]

Step 2: Standardize the Difference

Next, we standardize this difference by dividing it by the standard deviation ($\sigma$) of the distribution. \[ z = \frac{(9832 - 8427)}{1858} = \frac{1405}{1858} = 0.756 \]

Final Answer:

The $z$ score for the value $X=9832$ in the distribution, rounded to 2 decimal places, is 0.76. \[ z = 0.76 \]

Step 1: Calculate the Difference

To find the $z$ score for the value $X=12405$ in the distribution, we first calculate the difference from the mean ($\mu=10381$). \[ X - \mu = 12405 - 10381 = 2024 \]

Step 2: Standardize the Difference

Next, we standardize this difference by dividing it by the standard deviation ($\sigma$) of the distribution. \[ z = \frac{(12405 - 10381)}{2117} = \frac{2024}{2117} = 0.956 \]

Final Answer:

The $z$ score for the value $X=12405$ in the distribution, rounded to 2 decimal places, is 0.96. \[ z = 0.96 \]

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