Question

The annual salaries of all employees at a financial company are normally distributed with a mean = $43,000 and a standard deviation = $4,500. What is the z-score of a company employee who makes an annual salary of $33,000?

a) -2.22
b) -1.78
c) -1.33
d) -0.89

Answer 1

The z-score for an employee earning an annual salary of $33,000 with a mean salary of $43,000 and a standard deviation of $4,500 is -2.22.

Step-by-step explanation:

The student asked about calculating a z-score for a company employee making an annual salary of $33,000 when the mean is $43,000 and the standard deviation is $4,500. The z-score is found using the formula:

z = (X - μ) / σ

where X is the value (salary in this case), μ is the mean, and σ is the standard deviation. Plugging in the values we get:

z = ($33,000 - $43,000) / $4,500

z = -$10,000 / $4,500

z = -2.22

Therefore, the z-score is -2.22, which corresponds to option (a).