The z-scores for a deta seller making $13 and $17 an hour will be [tex]Z_{13}=0.5 \ \ \ Z_{17}=2.5[/tex]
The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.
To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
Where x is the value of the data, μ is the mean and σ is the standard deviation
In this case :
μ = 12 $/h
[tex]\sigma[/tex] = 2 $/h
We need to calculate the Z-scores for x=17 and x=13
[tex]Z_{13}=\dfrac{13-12}{2}=0.5[/tex]
[tex]Z_{17}=\dfrac{17-12}{2}=2.5[/tex]
Thus the z-scores for a deta seller making $13 and $17 an hour will be [tex]Z_{13}=0.5 \ \ \ Z_{17}=2.5[/tex]
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