Respuesta :
Answer:
Due to the higher z-score, Reed performed better in relationship to their peers
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.
In this question:
Whoever had the higher z-score performed better in relation to their peers.
Maria:
Took the SAT, grade 1270, so [tex]X = 1270[/tex]
Mean score of 1060 with standard deviation of 195 (max score of 1600). This means that [tex]\mu = 1060, \sigma = 295[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1270 - 1060}{295}[/tex]
[tex]Z = 0.71[/tex]
Reed:
Took the ACT, score of 27, so [tex]X = 27[/tex]
Mean of 20.9 with standard deviation of 5.6, which means that [tex]\mu = 20.9, \sigma = 5.6[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27 - 20.9}{5.6}[/tex]
[tex]Z = 1.09[/tex]
Due to the higher z-score, Reed performed better in relationship to their peers
