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Sagot :
Answer:
Due to the higher Z-score, Kamala had the best GPA when compared to other students at her school.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
In this question:
Whichever student's GPA had the higher z-score had the best GPA compared to other students.
Thuy 2.5 3.2 0.8
This means that [tex]X = 2.5, \mu = 3.2, \sigma = 0.8[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 3.2}{0.8}[/tex]
[tex]Z = -0.875[/tex]
Vichet 88 75 20
This means that [tex]X = 88, \mu = 75, \sigma = 20[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{88 - 75}{20}[/tex]
[tex]Z = 0.65[/tex]
Kamala 8.9 8 0.4
This means that [tex]X = 8.9, \mu = 8, \sigma = 0.4[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.9 - 8}{0.4}[/tex]
[tex]Z = 2.25[/tex]
Due to the higher Z-score, Kamala had the best GPA when compared to other students at her school.
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