Answer:
On the SAT her z-score was 1.4
On the ACT her z-score was 1.5
Due to the higher z-score, she performed better on the ACT.
Step-by-step explanation:
The z-score measures how many standard deviations a score X is above or below the mean. it is given by the following formula:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
In which
is the mean and
is the standard deviation.
In this problem
We find her z-score for both the SAT and the ACT.
SAT
Exam Caitlin's Exam Score Mean Exam Score Standard Deviation
SAT 1850 1500 250
So ![X = 1850, \mu = 1500, \sigma = 250](https://tex.z-dn.net/?f=X%20%3D%201850%2C%20%5Cmu%20%3D%201500%2C%20%5Csigma%20%3D%20250)
![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{1850 - 1500}{250}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B1850%20-%201500%7D%7B250%7D)
![Z = 1.4](https://tex.z-dn.net/?f=Z%20%3D%201.4)
ACT
Exam Caitlin's Exam Score Mean Exam Score Standard Deviation
ACT 28 20.8 4.8
So ![X = 28, \mu = 20.8, \sigma = 4.8](https://tex.z-dn.net/?f=X%20%3D%2028%2C%20%5Cmu%20%3D%2020.8%2C%20%5Csigma%20%3D%204.8)
![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{28 - 20.8}{4.8}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B28%20-%2020.8%7D%7B4.8%7D)
![Z = 1.5](https://tex.z-dn.net/?f=Z%20%3D%201.5)
She wants to know on which test she performed better. Find the z-scores for her result on each exam.
On the SAT her z-score was 1.4
On the ACT her z-score was 1.5
Due to the higher z-score, she performed better on the ACT.