Question

Use z-scores to determine which score has the highest relative position: a score of 42.5 on a test for which the mean is 47 and standard deviation of 9, or a score of 2.5 on a test for which the mean is 4.2 and the standard deviation is 1.2 , or a score of 427.2 on a test for which the mean is 444 and the standard deviation is 42.

Answer 1

Answer

a) $\bar{X}=42.5 , \mu = 47 , \sigma = 9$

     $z_1 = \dfrac{\bar{X}-\mu}{\sigma}$

     $z_1 = \dfrac{42.5-47}{9}$

           z₁ = -0.5

b) $\bar{X}=2.5 , \mu = 4.2 , \sigma = 1.2$

     $z_2 = \dfrac{\bar{X}-\mu}{\sigma}$

     $z_2= \dfrac{2.5-4.2}{1.2}$

           z₂ = -1.42

c) $\bar{X}=427.2 , \mu = 444 , \sigma = 42$

     $z_3 = \dfrac{\bar{X}-\mu}{\sigma}$

     $z_3 = \dfrac{427.2-444}{42}$

           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