We need to find the z-score for each value of x given.
The z-score z of value x belonging to a population with mean μ and standard deviation σ is defined as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]In this problem, we have:
[tex]\begin{gathered} \mu=40 \\ \\ \sigma=8 \end{gathered}[/tex]Thus, for each value of x given, we obtain:
[tex]\begin{gathered} z(x=44)=\frac{44-40}{8}=\frac{4}{8}=0.5 \\ \\ z(x=38)=\frac{38-40}{8}=\frac{-2}{8}=-0.25 \\ \\ z(x=48)=\frac{48-40}{8}=\frac{8}{8}=1 \\ \\ z(x=34)=\frac{34-40}{8}=\frac{-6}{8}=-0.75 \\ \\ z(x=56)=\frac{56-40}{8}=\frac{16}{8}=2 \\ \\ z(x=32)=\frac{32-40}{8}=\frac{-8}{8}=-1 \end{gathered}[/tex]Answer
X = 44: 0.5
X = 38: -0.25
X = 48: 1
X = 34: -0.75
X = 56: 2
X = 32: -1
