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?

Answer 1

Answer:

$z=5$

Step-by-step explanation:

We have been given that the 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.

To solve our given problem we will use z-score formula.

$z=\frac{x-\mu}{\sigma}$ where,

$z=\text{z-score}$,

$x=\text{Sample score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$

Upon substituting our given values in z-score formula we will get,

$z=\frac{54,000-34,000}{4,000}$

$z=\frac{20,000}{4000}$

$z=5$

Therefore, the z-score of a company employee who makes an annual salary of $54,000 is 5.

Answer 2

The z-score is defined as the number of standard deviations above or below the mean. In this case, since the actual value is above the mean, we expect z > 0.
We calculate z using the equation: $z=\frac{x-\mu}{SD}=\frac{54000-34000}{4000}=\frac{20000}{4000}=5$