Respuesta :
Answer:
Tera had the higher z-score, so she 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 problem:
Whoever has the higher z-score should get the job.
Brittany:
Scored 88.3, mean 63.1, standard deviation 14. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{88.3 - 63.1}{14}[/tex]
[tex]Z = 1.8[/tex]
Alissa:
Scored 236.5, mean 219, standard deviation 25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{236.5 - 219}{25}[/tex]
[tex]Z = 0.7[/tex]
Tera:
Scored 7.75, mean 6.66, standard deviation 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.75 - 6.66}{0.5}[/tex]
[tex]Z = 2.18[/tex]
Tera had the higher z-score, so she should be offered the job.
