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

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=(x-\mu)/(SD)=(54000-34000)/(4000)=(20000)/(4000)=5`

Answer 2

`z=5`

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=(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=(54,000-34,000)/(4,000)`

`z=(20,000)/(4000)`

`z=5`

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