The average student loan debt for college graduates is $25,600. Suppose that that distribution is normal and that the standard deviation is $10,500. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar. %3D a. What is the distribution of X? X ~ N( b Find the probability that the college graduate has between $10,400 and $17,400 in student loan debt. c. The middle 20% of college graduates' loan debt lies between what two numbers? Low: $ High: $

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Normal Distribution 

**Understanding Student Loan Debt Distribution**

The average student loan debt for college graduates is $25,600. This debt follows a normal distribution, with a standard deviation of $10,500. Let X represent the student loan debt of a randomly selected college graduate. Instructions below will guide you through understanding this distribution and computing probabilities. Ensure all probabilities are rounded to four decimal places and all dollar amounts to the nearest dollar.

a. **Determine the Distribution of X:**

   X follows a normal distribution denoted as X ~ N(____, ____).

b. **Calculate the Probability:**

   What is the probability that a college graduate's debt is between $10,400 and $17,400?

   Probability: __________

c. **Middle 20% of College Graduates' Loan Debt:**

   Identify the loan debt values that capture the middle 20% of college graduates' debt.

   Low: $________

   High: $________

Use this guide to understand the student loan debt trends and perform statistical calculations related to the distribution.
Transcribed Image Text:**Understanding Student Loan Debt Distribution** The average student loan debt for college graduates is $25,600. This debt follows a normal distribution, with a standard deviation of $10,500. Let X represent the student loan debt of a randomly selected college graduate. Instructions below will guide you through understanding this distribution and computing probabilities. Ensure all probabilities are rounded to four decimal places and all dollar amounts to the nearest dollar. a. **Determine the Distribution of X:** X follows a normal distribution denoted as X ~ N(____, ____). b. **Calculate the Probability:** What is the probability that a college graduate's debt is between $10,400 and $17,400? Probability: __________ c. **Middle 20% of College Graduates' Loan Debt:** Identify the loan debt values that capture the middle 20% of college graduates' debt. Low: $________ High: $________ Use this guide to understand the student loan debt trends and perform statistical calculations related to the distribution.
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