MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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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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