Question

How many standard deviations is each student away from hiir school average? If the student GPA is higher than his school average, enter this as a positive number. If the student GPA is lower than his school average, enter this as a negative number.

Answer 1

Part A: Thuy

mean (average) of 2.8, and a standard deviation of 0.8

Thuy's score is 2.5

Calculate the z-score and we have

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{2.5-2.8}{0.8} \\ z=\frac{-0.3}{0.8} \\ z=-0.375 \end{gathered}$

Therefore, Thuy is -0.375 standard deviations away from the mean.

Part B: Vichet

Doing the same as above, we have the following values

x = 86

μ = 78

σ = 10

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{86-78}{10} \\ z=\frac{8}{10} \\ z=0.8 \end{gathered}$

Therefore, Vichet is 0.8 standard deviations away from the mean.

Part C: Kamala

x = 8.5

μ = 8.4

σ = 0.5

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{8.5-8.4}{0.5} \\ z=\frac{0.1}{0.5} \\ z=0.2 \end{gathered}$

Therefore, Kamala is 0.2 standard deviations away from the mean.