Question

The annual salaries of all employees at a financial company are normally distributed with a mean mc014-1.jpg = $34,000 and a standard deviation mc014-2.jpg = $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?

Answer 1

Answer:

The z-score of a company employee who makes an annual salary of $28,000 is -1.5

Step-by-step explanation:

We know that,

$Z=\dfrac{X-\mu}{\sigma}$

where,

Z = Z score,

X = raw score = 28,000

μ = mean = 34,000

σ = standard deviation = 4,000

Putting the values,

$Z=\dfrac{28000-34000}{4000}=\dfrac{-6000}{4000}=-1.5$

Negative sign is there, because the salary is below than the mean salary.

Answer 2

The z-score of a company employee who makes an annual salary of $28,000 is -1.5.

Z score

Z score is used to show by how many standard deviations the raw score is above or below the mean. it is given by:

$z=\frac{x-\mu}{\sigma} \\ \\ Where\ \mu=mean, x=raw \ score, \sigma=standard\ deviation$

Given that:

• μ = $34000, σ = 4000.

For x = 28000:

• $z=\frac{28000-34000}{4000} =-1.5$

The z-score of a company employee who makes an annual salary of $28,000 is -1.5.

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