Respuesta :
Answer:
Due to the higher Z-score, Demetria 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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
In this question:
Whichever applicant had grade with the highest z-score should be offered the job.
Demetria got a score of 85.1; this version has a mean of 61.1 and a standard deviation of 12.
For Demetria, we have [tex]X = 85.1, \mu = 61.1, \sigma = 12[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{85.1 - 61.1}{12}[/tex]
[tex]Z = 2[/tex]
Vincent got a score of 299.2; this version has a mean of 264 and a standard deviation of 22.
For Vincent, we have [tex]X = 299.2, \mu = 264, \sigma = 22[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{299.2 - 264}{22}[/tex]
[tex]Z = 1.6[/tex]
Tobias got a score of 7.26; this version has a mean of 7.1 and a standard deviation of 0.4.
For Tobias, we have [tex]X = 7.26, \mu = 7.1, \sigma = 0.4[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.26 - 7.1}{0.4}[/tex]
[tex]Z = 0.4[/tex]
Due to the higher Z-score, Demetria should be offered the job.
