Answer:
Due to the higher Z-score, Demetria should be offered the job.
Step-by-step explanation:
Z-score:
In a set with mean
and standard deviation
, the z-score 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 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
. 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{85.1 - 61.1}{12}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B85.1%20-%2061.1%7D%7B12%7D)
![Z = 2](https://tex.z-dn.net/?f=Z%20%3D%202)
Vincent got a score of 299.2; this version has a mean of 264 and a standard deviation of 22.
For Vincent, we have
.
![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{299.2 - 264}{22}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B299.2%20-%20264%7D%7B22%7D)
![Z = 1.6](https://tex.z-dn.net/?f=Z%20%3D%201.6)
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
.
![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{7.26 - 7.1}{0.4}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B7.26%20-%207.1%7D%7B0.4%7D)
![Z = 0.4](https://tex.z-dn.net/?f=Z%20%3D%200.4)
Due to the higher Z-score, Demetria should be offered the job.
This construction called a pencil of lines. That figure can have 3,4,5.... any number of straights lines. The main rule is their common point. And it looks like spokes of a wheel. Here you can find a lot of vertical angles and rays.
The answer is C: Lincoln uses 25 cents worth of supplies per cup.