Question

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A census study was conducted on base salary of brand managers in Houston, TX as well as in Los Angeles, CA. The data shows both of them to be normally distributed. The average base salary for a brand manager in Houston, Texas, is $89,250 and the average base salary for a brand manager in Los Angeles, California, is $99,500. The standard deviation for the salaries brand managers in Houston is $21,325, and the standard deviation for brand managers in Los Angeles is $19,675.

Part A: Ms. Jane Roberts is a Brand Manager to be relocated to in Houston, TX. In order make the offer attractive to her, how much should Ms. Jane Roberts be offered so that her salary is what 92.5% of the brand managers earn in Los Angeles, CA?

Part B: What percentage of brand managers in Houston earn a salary that is higher than what Ms. Jane Roberts is to be offered?

Answer 1

A. 92.5% of the brand managers in Los Angeles earn less than or equal to (=NORM.INV(0.925,99500,19675)) = $ 127,822.78

Hence Ms Jane Roberts should be offered a salary higher than or equal to $ 127,822.78

B. The salary of $ 127,822.78 corresponds to (=NORM.DIST(127822.78,89250,21325,TRUE)) = 0.9648 of the salary distribution in Houston.

We can conclude that 96.48% of the managers in Houston earn less than or equal to $ 127,822.78

100-96.48 = 3.52% of the managers in Houston earn a salary higher than what Ms Jane Roberts is to be offered.