# 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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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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Step 1

The z-score is defined as follows:

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:

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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