Answer:
Due to the higher z-score, she should report her ACT grade.
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.
Which should she report
The grade with the higher z-score.
SAT:
Scored 610, mean 515, standard deviation 114. So [tex]X = 610, \mu = 515, \sigma = 114[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{610 - 515}{114}[/tex]
[tex]Z = 0.83[/tex]
ACT:
Scored 27, mean 21, standard deviation 5.1. So [tex]X = 27, \mu = 21, \sigma = 5.1[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27 - 21}{5.1}[/tex]
[tex]Z = 1.18[/tex]
Due to the higher z-score, she should report her ACT grade.
