Question

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 TWO decimal places.)

Answer 1

Answer: 1.79

Step-by-step explanation:

Let x = hourly wage for a social worker. Then, the z-score for x is given by


`\text{z - score} = (x - \mu)/(\sigma)`

where


`\mu = \text{ mean hourly wage of a social worker }= \$ 28.08 \\ \sigma = \text{ standard deviation of the wage of the social worker }= \$ 1.97`

Since Jeronica's salary is $31.60, the z-score of Jeronica's is given by


`\text{z - score} = (x - \mu)/(\sigma) \\ \\ \text{z - score} = (31.60 - 28.08)/(1.97) \\ \\ \boxed{\text{z - score} = 1.79}`