Answer:
Since they have different z-scores, they are not earning relatively the same.
Step-by-step explanation:
We use z-scores to solve this question.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In this question:
They will be earning relatively the same if they have the same z-score.
Tokyo:
Earns 460, mean 420, standard deviation 20. So [tex]X = 460, \mu = 420, \sigma = 20[/tex]. The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{460 - 420}{20}[/tex]
[tex]Z = 2[/tex]
Hamburg:
Earns 3300, mean 3200, standard deviation 57. So [tex]\mu = 3300, \sigma = 3200, \sigma = 57[/tex].
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3300 - 3200}{57}[/tex]
[tex]Z = 1.75[/tex]
Since they have different z-scores, they are not earning relatively the same.
