Given -
Kaitlyn Score = 78.2
Kaitlyn Mean = 73.8
Standard deviation = 11
Rebecca score = 256.3
Rebecca mean = 236
Standard deviation = 29
Tera score = 7.24
Tera mean = 6.7
Standard deviation = 0.9
To Find -
Which of the applicants should be offered the job =?
Step-by-Step Explanation :
We know, the formula for z-score:
[tex]\begin{gathered} z-score\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \\ Where,\text{ x = Score} \\ \mu\text{ = Mean} \\ \sigma\text{ = Standard Deviation} \\ \\ \end{gathered}[/tex]
z-score of kaitlyn =
[tex]\begin{gathered} z-score\text{ = }\frac{78.2-73.8}{11} \\ \\ z-score\text{ = }\frac{4.4}{11}\text{ = 0.4} \end{gathered}[/tex]
z-score of Rebecca =
[tex]\begin{gathered} z-score\text{ = }\frac{256.3-236}{29} \\ \\ z-score\text{ = }\frac{20.3}{29}\text{ = 0.7} \end{gathered}[/tex]
z-score of Tera =
[tex]\begin{gathered} z-score\text{ = }\frac{7.24-6.7}{0.9} \\ \\ z-score\text{ = }\frac{0.54}{0.9}\text{ = 0.6} \\ \\ \end{gathered}[/tex]
Now,
The applicant with the highest z-score is most likely to be offered the job.
Rebecca has the highest z-score of 0.7
Final Answer -
Rebecca should be offered the job.
