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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?

Respuesta :

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: [tex]z=\frac{x-\mu}{SD}=\frac{54000-34000}{4000}=\frac{20000}{4000}=5[/tex]

Answer:

[tex]z=5[/tex]

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.

[tex]z=\frac{x-\mu}{\sigma}[/tex] where,

[tex]z=\text{z-score}[/tex],

[tex]x=\text{Sample score}[/tex],

[tex]\mu=\text{Mean}[/tex],

[tex]\sigma=\text{Standard deviation}[/tex]

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

[tex]z=\frac{54,000-34,000}{4,000}[/tex]

[tex]z=\frac{20,000}{4000}[/tex]

[tex]z=5[/tex]

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

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