5. Relationships between means, standard deviations, X values, and z-scores The

Question

5. Relationships between means, standard deviations, X values, and z-scores 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 Canada who makes $2,063.30 has a z-score of +0.50 relative to other computer programmers in Canada and that the standard deviation of the salary of computer programmers in Canada is $458.60. The average salary, then, for computer programmers in Canada is Suppose you are also told that a computer programmer in Portugal who makes $1,387.40 has a z-score of +2.00 relative to other computer programmers in Portugal and that the mean of the salary of computer programmers in Portugal is $925. The standard deviation of the salary, then, for computer programmers in Portugal is

Explanation / Answer

Result:

We know that z = (x-µ)/

From the given information,

0.50 = (2063.30- µ)/458.60

µ = 2063.30 - 0.50*458.60

=1834.0

Second part

From the given information,

2.0 =(1387.40-925)/

= (1387.40-925)/2.0

= 231.2

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