Suppose a computer programmer in each of the five countries listed is offered a salary of $1500 per month. Using the z-scores and assuming that computer programmer prefers a salary that has a higher relative value, the computer programmer from what country will likely be the most pleased with the offer
Suppose a computer programmer in each of the five countries listed is offered a salary of $1500 per month. Using the z-scores and assuming that computer programmer prefers a salary that has a higher relative value, the computer programmer from what country will likely be the most pleased with the offer
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Suppose a computer programmer in each of the five countries listed is offered a salary of $1500 per month. Using the z-scores and assuming that computer programmer prefers a salary that has a higher relative value, the computer programmer from what country will likely be the most pleased with the offer?
![**Average Monthly Salaries and Standard Deviations by Country**
The table below provides information on the average monthly salaries in US dollars for various countries, along with the standard deviation for these salaries. Additionally, it includes the Z-score calculation for a salary of $1500, using the formula:
\[ \text{Z-score} = \frac{X - \mu}{\sigma} \]
where:
- \(X\) is $1500,
- \(\mu\) is the average monthly salary,
- \(\sigma\) is the standard deviation.
| Country | Average Monthly Salary (USD) | Standard Deviation (USD) | Z-score |
|-------------------|------------------------------|--------------------------|-------------|
| Italy | $1557 | $467.20 | -0.122 |
| Hungary | $1468 | $220.20 | 0.15 |
| Czech Republic | $1059 | $158.80 | 2.78 |
| United States | $4141 | $1242.20 | -2.13 |
| Latvia | $790 | $118.60 | 5.99 |
**Interpretation of the Z-scores:**
- A Z-score less than 0 indicates the average salary is higher than $1500.
- A Z-score greater than 0 indicates the average salary is lower than $1500.
- The magnitude of the Z-score indicates how many standard deviations away $1500 is from the average salary.
For example, Latvia has a Z-score of 5.99, suggesting that $1500 is significantly higher than the average salary in Latvia, by approximately 5.99 standard deviations. Conversely, the United States has a Z-score of -2.13, implying that the average monthly salary is much higher than $1500.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff887d5a5-eeaa-4205-bd97-87ce3abe5fbf%2F150e078f-1736-401d-965b-7f49319d0188%2F8ub8lxm_processed.png&w=3840&q=75)
Transcribed Image Text:**Average Monthly Salaries and Standard Deviations by Country**
The table below provides information on the average monthly salaries in US dollars for various countries, along with the standard deviation for these salaries. Additionally, it includes the Z-score calculation for a salary of $1500, using the formula:
\[ \text{Z-score} = \frac{X - \mu}{\sigma} \]
where:
- \(X\) is $1500,
- \(\mu\) is the average monthly salary,
- \(\sigma\) is the standard deviation.
| Country | Average Monthly Salary (USD) | Standard Deviation (USD) | Z-score |
|-------------------|------------------------------|--------------------------|-------------|
| Italy | $1557 | $467.20 | -0.122 |
| Hungary | $1468 | $220.20 | 0.15 |
| Czech Republic | $1059 | $158.80 | 2.78 |
| United States | $4141 | $1242.20 | -2.13 |
| Latvia | $790 | $118.60 | 5.99 |
**Interpretation of the Z-scores:**
- A Z-score less than 0 indicates the average salary is higher than $1500.
- A Z-score greater than 0 indicates the average salary is lower than $1500.
- The magnitude of the Z-score indicates how many standard deviations away $1500 is from the average salary.
For example, Latvia has a Z-score of 5.99, suggesting that $1500 is significantly higher than the average salary in Latvia, by approximately 5.99 standard deviations. Conversely, the United States has a Z-score of -2.13, implying that the average monthly salary is much higher than $1500.
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