The year Deshaun graduated college, the starting salaries of all entry-level software engineers in the United States had a mean of $90,000 and a standard deviation of $3300. That year, Deshaun got a job as an entry-level software engineer working for a firm in the United States. His starting salary was $93,500.Find the z-score of Deshaun's starting salary relative to the starting salaries among all the entry-level software engineers in the United States for the year Deshaun graduated. Round your answer to two decimal places.
Question
The year Deshaun graduated college, the starting salaries of all entry-level software engineers in the United States had a mean of 3300. That year, Deshaun got a job as an entry-level software engineer working for a firm in the United States. His starting salary was $93,500.Find the z-score of Deshaun's starting salary relative to the starting salaries among all the entry-level software engineers in the United States for the year Deshaun graduated. Round your answer to two decimal places.
Solution
To find the z-score, we need to subtract the mean from the given value and then divide by the standard deviation.
Here's the step-by-step calculation:
- Subtract the mean salary from Deshaun's salary: 90,000 = $3,500
- Divide the difference by the standard deviation: 3,300
Let's calculate it:
3,500 / 3,300 = 1.0606060606060606
Rounding to two decimal places, the z-score is 1.06. This means Deshaun's starting salary was 1.06 standard deviations above the mean starting salary for entry-level software engineers in the United States the year he graduated.
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