Questions: The year Teresa graduated college, the starting salaries of all entry-level software engineers in the United States had a mean of 92,000 and a standard deviation of 1080. That year, Teresa got a job as an entry-level software engineer working for a firm in the United States. Her starting salary was 89,000. (a) Find the z-score of Teresa's starting salary relative to the starting salaries among all the entry-level software engineers in the United States for the year Teresa graduated. Round your answer to two decimal places. [ z=square ] (b) Fill in the blanks to interpret the z-score of Teresa's starting salary. Make sure to express your answer in terms of a positive number of standard deviations. Teresa's starting salary was standard deviations (Choose one) V the mean starting salary of all entry-level software engineers in the United States.

The year Teresa graduated college, the starting salaries of all entry-level software engineers in the United States had a mean of 92,000 and a standard deviation of 1080. That year, Teresa got a job as an entry-level software engineer working for a firm in the United States. Her starting salary was 89,000. (a) Find the z-score of Teresa's starting salary relative to the starting salaries among all the entry-level software engineers in the United States for the year Teresa graduated. Round your answer to two decimal places. [ z=square ] (b) Fill in the blanks to interpret the z-score of Teresa's starting salary. Make sure to express your answer in terms of a positive number of standard deviations. Teresa's starting salary was standard deviations (Choose one) V the mean starting salary of all entry-level software engineers in the United States.
Transcript text: The year Teresa graduated college, the starting salaries of all entry-level software engineers in the United States had a mean of $\$ 92,000$ and a standard deviation of $\$ 1080$. That year, Teresa got a job as an entry-level software engineer working for a firm in the United States. Her starting salary was $\$ 89,000$. (a) Find the $z$-score of Teresa's starting salary relative to the starting salaries among all the entry-level software engineers in the United States for the year Teresa graduated. Round your answer to two decimal places. \[ z=\square \] (b) Fill in the blanks to interpret the $z$-score of Teresa's starting salary. Make sure to express your answer in terms of a positive number of standard deviations. Teresa's starting salary was standard deviations (Choose one) $\mathbf{V}$ the mean starting salary of all entrylevel software engineers in the United States.
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Solution

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Solution Steps

To find the zz-score of Teresa's starting salary, we use the formula for the zz-score: z=X−μσ z = \frac{X - \mu}{\sigma} , where X X is Teresa's salary, μ \mu is the mean salary, and σ \sigma is the standard deviation. For part (b), interpret the zz-score by determining how many standard deviations Teresa's salary is from the mean and whether it is above or below the mean.

Step 1: Calculate the zz-score

To find the zz-score of Teresa's starting salary, we use the formula:

z=X−μσ z = \frac{X - \mu}{\sigma}

where:

  • X=89000 X = 89000 (Teresa's salary),
  • μ=92000 \mu = 92000 (mean salary),
  • σ=1080 \sigma = 1080 (standard deviation).

Substituting the values, we get:

z=89000−920001080=−30001080≈−2.778 z = \frac{89000 - 92000}{1080} = \frac{-3000}{1080} \approx -2.778

Step 2: Interpret the zz-score

The zz-score of −2.778-2.778 indicates that Teresa's starting salary is approximately 2.7782.778 standard deviations below the mean starting salary of all entry-level software engineers in the United States.

Final Answer

(a) The zz-score of Teresa's starting salary is −2.78\boxed{-2.78}.

(b) Teresa's starting salary was 2.78\boxed{2.78} standard deviations below the mean starting salary of all entry-level software engineers in the United States.

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