According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to 2 decimal places.)
Question
According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was 1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to 2 decimal places.)
Solution 1
To calculate the z-score, we need to use the formula:
Z = (X - μ) / σ
where: X = value (Jeronica's wage) μ = mean (average wage) σ = standard deviation
Given in the problem: X = 28.08 σ = $1.97
Substituting these values into the formula, we get:
Z = (28.08) / $1.97
Performing the subtraction in the numerator:
Z = 1.97
Finally, dividing the numerator by the denominator gives us the z-score.
Z = 1.79 (rounded to two decimal places)
So, Jeronica's z-score is 1.79. This means her wage is 1.79 standard deviations above the mean wage for a social worker.
Solution 2
To calculate the z-score, we need to use the formula:
Z = (X - μ) / σ
where: X = value (Jeronica's wage) μ = mean (average wage) σ = standard deviation
Given in the problem: X = 28.08 σ = $1.97
Substitute these values into the formula:
Z = (28.08) / 3
Solution 3
To calculate the z-score, we need to use the formula:
Z = (X - μ) / σ
where:
- X is the value we're comparing (Jeronica's wage)
- μ is the mean (average wage)
- σ is the standard deviation
Let's plug in the values:
Z = (28.08) / $1.97
Solution 4
To calculate the z-score, we need to subtract the mean from the individual score (in this case, Jeronica's wage), and then divide that by the standard deviation.
Here's the step-by-step calculation:
- Subtract the mean wage from Jeronica's wage: 28.08 = $3.52
- Divide the difference by the standard deviation: 1.97 = 1.786
So, Jeronica's z-score is 1.79 (rounded to two decimal places). This means her wage is 1.79 standard deviations above the mean wage for social workers.
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