Question

the annual salaries of all employees at a financial company are normally distributed with a mean of $34,000 and a standard deviation of $4,000. what is the z - score of a company employee who makes an annual salary of $54,000?
-5
-3
4
5

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the mean of the dataset, and $\sigma$ is the standard deviation of the dataset.

Step2: Identify values

We are given that $x = 54000$, $\mu=34000$, and $\sigma = 4000$.

Step3: Substitute values into formula

Substitute the values into the z - score formula: $z=\frac{54000 - 34000}{4000}$.
First, calculate the numerator: $54000-34000 = 20000$.
Then, divide by the standard deviation: $\frac{20000}{4000}=5$.

Answer:

5