Kathy and Linda both accepted new jobs at different companies. Kathy's starting salary is $31,500 and Linda's starting salary is $33,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers. A website that collects salary information from a sample of employees for a number of major employers reports that Kathy's company offers a mean salary of $42,000 with a standard deviation of $7,000. Linda's company offers a mean salary of $45,000 with a standard deviation of $6,000. Find the z-scores corresponding to each woman's starting salary.

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Asked Aug 31, 2019
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Kathy and Linda both accepted new jobs at different companies. Kathy's starting salary is $31,500 and Linda's starting salary is $33,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers. A website that collects salary information from a sample of employees for a number of major employers reports that Kathy's company offers a mean salary of $42,000 with a standard deviation of $7,000. Linda's company offers a mean salary of $45,000 with a standard deviation of $6,000. Find the z-scores corresponding to each woman's starting salary.

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Expert Answer

Step 1

The z-score is defined as follows:

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Data value-mean 2-score Standard deviation

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Step 2

z-score for Kathy:

Kathy’s starting salary is $31,500. The mean salary is $42,000 with standard deviation of $7,000.

Thus, the data value is 31,500 with mean 42,000 and standard deviation 7,000.

The z-score is obtained as –1.5 in the following steps:

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-sCore 31500-42,000 7,000 =-1.5

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Step 3

z-score for Linda:

Linda’s starting salary is $33,000. The mean salary is $45,000 with standard deviation of $6,000.

Thus, the data value is 33,000 wit...

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-SCore33.000-45,000 6,000 =-2.0

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