Question

The International Average Salary Income Database provides a comparison of average salaries for various professions. The data are gathered from publications and reports obtained directly from government agencies (such as the U.S. Bureau of Labor Statistics) or from the International Labour Organization. Suppose you are told that a computer programmer in Portugal who makes $578.20 has a z-score of -1.50 relative to other computer programmers in Portugal and that the standard deviation of the salary of computer programmers in Portugal is $231.20. The average salary, then, for computer programmers in Portugal is. Suppose you are also told that a computer programmer in Mexico who makes $952.40 has a z-score of +0.50 relative to other computer programmers in Mexico and that the mean of the salary of computer programmers in Mexico is $886. The standard deviation of the salary, then, for computer programmers in Mexico is .

Answer 1

a) The average salary for computer programmers in Portugal is $925.

b) The standard deviation of the salary of computer programmers is $132.8

Explanation:

We are given the following in the question:

a) Standard Deviation, σ = $231.20

We are given that the distribution of salary of computer programmers is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

Putting values, we get,

`-1.50 = \displaystyle(578.20-\mu)/(231.20)\\\\\mu = 1.50(231.20) + 578.20\\\Rightarrow \mu = 925`

Thus, the average salary for computer programmers in Portugal is $925.

b) Mean, μ = $886

We are given that the distribution of salary of computer programmers is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

Putting values, we get,

`0.50 = \displaystyle(952.40-886)/(\sigma)\\\\\sigma= (952.40-886)/(0.50)\\\\\sigma = 132.8`

Thus, the standard deviation of the salary of computer programmers is $132.8