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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.

Respuesta :

Eduard22sly

1. The z-scores corresponding to Kathy's starting salary is -1.5

2. The z-scores corresponding to Linda's starting salary is -2

z-score

z = (x - μ) / σ

Where

  • z is the s-score
  • x is the score
  • μ is the mean
  • σ is the standard deviation

1. How to determine the z-score for Kathy's starting salary

  • Starting salary (x) = $ 31500
  • Mean salary (μ) = $ 42000
  • Standard deviation (σ) = $ 7000
  • z-score for Kathy's starting salary (z) =?

z = (x - μ) / σ

z = (31500 - 42000) / 7000

z-score for Kathy's starting salary = -1.5

2. How to determine the z-score for Linda's starting salary

  • Starting salary (x) = $ 33000
  • Mean salary (μ) = $ 45000
  • Standard deviation (σ) = $ 6000
  • z-score for Linda's starting salary (z) =?

z = (x - μ) / σ

z = (33000 - 45000) / 6000

z-score for Linda's starting salary = -2

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