Question

Three students were applying to the same graduate school. They came from schools with different grading systems. Student GPA Scool Average GPA School Standard DeviationThuy 3.4 2.8 0.3Vichet 3.5 3.5 0.4Kamala 82 86 4Which student had the best GPA when compared to his school? Explain how you determined your answer.

Answer 1

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

`Z=(x-\mu)/(\sigma)`

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

`Z=(3.4-2.8)/(0.3)=(0.6)/(0.3)=2`

Thuy's z-score is 2.

Vichet's z-score:

x = 3.5

μ = 3.5

σ = 0.4

`Z=(3.5-3.5)/(0.4)=(0)/(0.4)=0`

Vichet's z-score is 0.

Kamala's z-score:

x = 82

μ = 86

σ = 4

`Z=(82-86)/(4)=(-4)/(4)=-1`

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.