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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?

Verified Answer :

Blitztiger

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: \(z=\frac{x-\mu}{SD}=\frac{54000-34000}{4000}=\frac{20000}{4000}=5\)

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.

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