At a neighboring university, the average salary is also $45,000 and the distribution is normal. If $47,000 has a z score of 1.5, what is the standard deviation?
Use the z-score formula to solve for standard deviation.
z = (x - mean)/sd
1.5 = (47000 - 45000)/sd
I'll let you take it from here.
3000
To find the standard deviation, we can use the formula for calculating z-scores:
z = (x - μ) / σ
Where:
z = z-score,
x = raw score,
μ = mean,
σ = standard deviation
Given that $47,000 has a z-score of 1.5, we can set up the equation:
1.5 = (47000 - 45000) / σ
Simplifying the equation:
1.5 = 2000 / σ
To solve for σ, we can cross-multiply:
1.5σ = 2000
Now, divide both sides by 1.5:
σ = 2000 / 1.5
Calculating this:
σ ≈ 1333.33
Therefore, the standard deviation is approximately $1333.33.
To find the standard deviation, we need to use the formula for calculating the z-score:
z = (x - μ) / σ
where:
- z is the z-score
- x is the raw score
- μ is the mean (average)
- σ is the standard deviation
In this case, we know that the z-score is 1.5 and the raw score (x) is $47,000. We are also given that the average salary (μ) is $45,000.
Plugging in the values into the formula, we get:
1.5 = (47000 - 45000) / σ
Now, we can solve for the standard deviation (σ):
1.5σ = 2000
Dividing both sides of the equation by 1.5:
σ = 2000 / 1.5
σ ≈ 1333.33
Therefore, the standard deviation is approximately $1333.33.