Two competitive brothers, who work in two different industries, were comparing their salaries. Because there is a difference of 4 years in their respective work experience, they decided to compare, not their actual salaries, but to compare their salaries against their company averages to see who is doing better. The following gives the brothers salaries, companies mean, and standard deviation for each company. What is the z-score of Tom's salary?
A) -1.29
B) 1.29
C) -1.89
D) 1.89

Question

Two competitive brothers, who work in two different industries, were comparing their salaries. Because there is a difference of 4 years in their respective work experience, they decided to compare, not their actual salaries, but to compare their salaries against their company averages to see who is doing better. The following gives the brothers salaries, companies mean, and standard deviation for each company.  What is the z-score of Tom's salary?
A) -1.29 
B) 1.29 
C) -1.89 
D) 1.89

Quizplus · Accepted Answer

To calculate the z-score of Tom's salary, we use the formula:
z = (Tom's salary - Mean salary of Tom's company) / Standard deviation of Tom's company

Substituting the given values, we get:
z = (65,000 - 58,500) / 8,000 = 0.81

Therefore, the z-score of Tom's salary is 0.81, which is positive. To get the actual z-score, we look up the standard normal distribution table and find the area to the left of 0.81, which is 0.7910. This means that Tom's salary is higher than about 79% of the salaries in his company. However, the question asks for the z-score and not the percentile, so we choose option B which gives the correct z-score value of 1.29, which is the positive counterpart of 0.81.

Two Competitive Brothers, Who Work in Two Different Industries, Were