Sure, let me guide you through the process of finding the z-score step-by-step.
The z-score measures how many standard deviations an element is from the mean. It is calculated using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where:
- [tex]\( X \)[/tex] is the value in the distribution (in this case, the employee's salary),
- [tex]\( \mu \)[/tex] is the mean of the distribution,
- [tex]\( \sigma \)[/tex] is the standard deviation of the distribution.
Given:
- The mean salary [tex]\(\mu = \$34,000\)[/tex],
- The standard deviation [tex]\(\sigma = \$4,000\)[/tex],
- The employee's salary [tex]\(X = \$28,000\)[/tex].
Now, we plug these values into the z-score formula:
1. Subtract the mean from the employee's salary:
[tex]\[
X - \mu = 28,000 - 34,000 = -6,000
\][/tex]
2. Divide this result by the standard deviation:
[tex]\[
z = \frac{-6,000}{4,000} = -1.5
\][/tex]
Therefore, the z-score of a company employee who makes an annual salary of $28,000 is [tex]\(-1.5\)[/tex].
So the correct answer is [tex]\(-1.5\)[/tex].
