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:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] 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 [tex]X = 1850, \mu = 1500, \sigma = 250[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1850 - 1500}{250}[/tex]
[tex]Z = 1.4[/tex]
ACT
Exam Caitlin's Exam Score Mean Exam Score Standard Deviation
ACT 28 20.8 4.8
So [tex]X = 28, \mu = 20.8, \sigma = 4.8[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 20.8}{4.8}[/tex]
[tex]Z = 1.5[/tex]
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.
