Question

Three students were applying to the same graduate school. They came from schools with different grading systems.

Answer 1

Thuy is -0.5 standard deviations from Thuy's school average.

Vichet is 0.5 standard deviations from Vichet's school average.

Kamala is 0.4 standard deviations from Kamala's school average.

Vichet is the student with the best GPA when compared to other students at his school

Step-by-step explanation

(A) To find how many standard deviations each student is from the school average, we have to find the z-score of each student using the formula:

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

where x = student GPA

μ = school average GPA

σ = school standard deviation

For Thuy, we have that the z-score is:

`\begin{gathered} z=(2.5-2.9)/(0.8)=(-0.4)/(0.8) \\ \\ z=-0.5 \end{gathered}`

For Vichet, we have that the z-score is:

`\begin{gathered} z=(88-83)/(10)=(5)/(10) \\ \\ z=0.5 \end{gathered}`

For Kamala, we have that the z-score is:

`\begin{gathered} z=(8.4-8.2)/(0.5)=(0.2)/(0.5) \\ \\ z=0.4 \end{gathered}`

Hence:

Thuy is -0.5 standard deviations from Thuy's school average.

Vichet is 0.5 standard deviations from Vichet's school average.

Kamala is 0.4 standard deviations from Kamala's school average.

(B) The student with the best GPA when compared to other students at his school is the student who has the highest z-score.

Hence, the student with the best GPA when compared to other students at his school is Vichet.