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
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{88.3 - 63.1}{14}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B88.3%20-%2063.1%7D%7B14%7D)
![Z = 1.8](https://tex.z-dn.net/?f=Z%20%3D%201.8)
Alissa:
Scored 236.5, mean 219, standard deviation 25. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{236.5 - 219}{25}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B236.5%20-%20219%7D%7B25%7D)
![Z = 0.7](https://tex.z-dn.net/?f=Z%20%3D%200.7)
Tera:
Scored 7.75, mean 6.66, standard deviation 0.5. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{7.75 - 6.66}{0.5}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B7.75%20-%206.66%7D%7B0.5%7D)
![Z = 2.18](https://tex.z-dn.net/?f=Z%20%3D%202.18)
Tera had the higher z-score, so she should be offered the job.