ANSWER and EXPLANATION
1) We want to find the z score for a student who had a GPA of 3.8.
To do this, we have to apply the formula for z score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where:
x = score/GPA
μ = mean
σ = standard deviation
Therefore, the z score for the student with a GPA of 3.8 is:
[tex]\begin{gathered} z=\frac{3.8-3}{0.6} \\ z=\frac{0.8}{0.6} \\ z=\text{1}.33 \end{gathered}[/tex]
2) The z score is a measure of how far away a data point is from the mean, in other words, it is a measure of how many standard deviations a data point is above or below a mean.
We can find how many standard deviations there are in a z score of -2.4 by dividing -2.4 by the standard deviation (0.6):
[tex]\begin{gathered} \frac{-2.4}{0.6} \\ -4 \end{gathered}[/tex]
Therefore, since the z score is negative, we can conclude that the student's GPA is 4 standard deviations below the mean value.
