Answer :
Answer:
Tobias should be offered the job.
Step-by-step explanation:
Z-score:
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]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
The applicant with the highest z-score should be chosen.
Tobias:
Score of 84.5, in a version with mean 66.9 and standard deviation 11. His z-score is found when [tex]X = 84.5, \mu = 66.9, \sigma = 11[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{84.5 - 66.9}{11}[/tex]
[tex]Z = 1.6[/tex]
Kiersten:
Score of 281.8, in a version with mean 261 and standard deviation 26. His z-score is found when [tex]X = 281.8, \mu = 261, \sigma = 26[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{281.8 - 261}{26}[/tex]
[tex]Z = 0.8[/tex]
Pierce:
Score of 7.69, version with mean 7.2 and standard deviation 0.7. His z-score is found when [tex]X = 7.69, \mu = 7.2, \sigma = 0.7[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.69 - 7.2}{0.7}[/tex]
[tex]Z = 0.7[/tex]
Due to the higher z-score, Tobias should be offered the job.
