Sociology graduates, upon entering the workforce are normally distributed and earn a mean salary of $30,000 with a standard deviation of $4000. 1. Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that randomly chosen salary exceeds $40,000? 2. Sam is not sure how much he will make upon graduation. He would be happy if his salary was in the middle 60% of salaries. Find the two salaries that are the cutoff values for the middle 60% of salaries.

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### Understanding Salary Expectations for Sociology Graduates

Sociology graduates, upon entering the workforce, earn a mean salary of $30,000. This salary distribution is normally distributed with a standard deviation of $4,000. Two example problems below help illustrate how we can use this information to answer questions about salary expectations:

#### Example Problem 1
**Jessica's Salary Aspirations:**
Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that a randomly chosen salary exceeds $40,000?

#### Example Problem 2
**Sam's Salary Concern:**
Sam is not sure how much he will make upon graduation. He would be happy if his salary was in the middle 60% of all sociology graduates' salaries. Find the two salaries that are the cutoff values for the middle 60% of salaries. 

These problems help students apply their understanding of normal distributions to real-world scenarios involving salary expectations.

#### Solving the Problems

To solve these problems, knowledge of the properties of the normal distribution and the Z-score table is required. For Jessica's problem, one would need to find the probability that a salary exceeds a certain value, while for Sam's problem, it involves finding the range of salaries that encompass the middle 60%.

These exercises can serve as practical applications of statistics in the social sciences, helping students to anticipate and plan for their financial futures based on educational outcomes.
Transcribed Image Text:### Understanding Salary Expectations for Sociology Graduates Sociology graduates, upon entering the workforce, earn a mean salary of $30,000. This salary distribution is normally distributed with a standard deviation of $4,000. Two example problems below help illustrate how we can use this information to answer questions about salary expectations: #### Example Problem 1 **Jessica's Salary Aspirations:** Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that a randomly chosen salary exceeds $40,000? #### Example Problem 2 **Sam's Salary Concern:** Sam is not sure how much he will make upon graduation. He would be happy if his salary was in the middle 60% of all sociology graduates' salaries. Find the two salaries that are the cutoff values for the middle 60% of salaries. These problems help students apply their understanding of normal distributions to real-world scenarios involving salary expectations. #### Solving the Problems To solve these problems, knowledge of the properties of the normal distribution and the Z-score table is required. For Jessica's problem, one would need to find the probability that a salary exceeds a certain value, while for Sam's problem, it involves finding the range of salaries that encompass the middle 60%. These exercises can serve as practical applications of statistics in the social sciences, helping students to anticipate and plan for their financial futures based on educational outcomes.
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