Respuesta :
Student GPA Scool | Average GPA School | Standard Deviation
Thuy 3.4 | 2.8 | 0.3
Vichet 3.5 | 3.5 | 0.4
Kamala 82 | 86 | 4
Let us find the z-score of each student then we will compare their z-scores.
Recall that the z-score is given by
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where x is the student's GPA, μ is the average GPA, and σ is the standard deviation.
Thuy's z-score:
x = 3.4
μ = 2.8
σ = 0.3
[tex]Z=\frac{3.4-2.8}{0.3}=\frac{0.6}{0.3}=2[/tex]Thuy's z-score is 2.
Vichet's z-score:
x = 3.5
μ = 3.5
σ = 0.4
[tex]Z=\frac{3.5-3.5}{0.4}=\frac{0}{0.4}=0[/tex]Vichet's z-score is 0.
Kamala's z-score:
x = 82
μ = 86
σ = 4
[tex]Z=\frac{82-86}{4}=\frac{-4}{4}=-1[/tex]Kamala's z-score is -1.
Comparison:
As you can see, Thuy's z-score is 2 standard deviation above the mean (positive z-score means above the mean) that is higher than other students.
Therefore, Thuy's GPA is best as compared to the other students.
