The annual salaries of all employees at a financial company are normally distributed with a mean = $34,000 and a standard deviation = $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?
34-28 = 6
so, it is 1.5 std away from the mean.
That should help if you know anything about the Z table.
To calculate the z-score, we can use the formula:
z = (x - μ) / σ
Where:
- z is the z-score,
- x is the value we want to find the z-score for,
- μ is the mean of the distribution, and
- σ is the standard deviation of the distribution.
Given:
μ = $34,000
σ = $4,000
x = $28,000
Now, we can substitute these values into the formula and calculate the z-score:
z = ($28,000 - $34,000) / $4,000
z = -$6,000 / $4,000
z = -1.5
So, the z-score of an employee with an annual salary of $28,000 is -1.5.
To find the z-score of an employee with an annual salary of $28,000 in a normally distributed population, we can use the formula for z-score:
z = (x - μ) / σ
where:
x = individual value
μ = mean of the population
σ = standard deviation of the population
In this case, the given values are:
x = $28,000
μ = $34,000
σ = $4,000
Substituting these values into the formula, we get:
z = (28,000 - 34,000) / 4,000
Simplifying the expression:
z = -6,000 / 4,000
z = -1.5
Therefore, the z-score of an employee who makes an annual salary of $28,000 is -1.5.