Answer
a) [tex]\bar{X}=42.5 , \mu = 47 , \sigma = 9[/tex]
[tex]z_1 = \dfrac{\bar{X}-\mu}{\sigma}[/tex]
[tex]z_1 = \dfrac{42.5-47}{9}[/tex]
z₁ = -0.5
b) [tex]\bar{X}=2.5 , \mu = 4.2 , \sigma = 1.2[/tex]
[tex]z_2 = \dfrac{\bar{X}-\mu}{\sigma}[/tex]
[tex]z_2= \dfrac{2.5-4.2}{1.2}[/tex]
z₂ = -1.42
c) [tex]\bar{X}=427.2 , \mu = 444 , \sigma = 42[/tex]
[tex]z_3 = \dfrac{\bar{X}-\mu}{\sigma}[/tex]
[tex]z_3 = \dfrac{427.2-444}{42}[/tex]
z₃ = -0.4
The better relative position score will be more standard deviations above the mean.
Higher the Z-score better is the relative position
hence, z₂ has highest relative position
