Answer :
Z score ( X = 1890 ): 1.31
Z score ( X = 1230 ): -0.76
Z score ( X = 2220 ): 2.34 (This value of Z is unusual )
Z score ( X = 1360 ): -0.35
Step-by-step explanation:
Here we have , A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1473 and the standard deviation was 318 . The test scores of four students selected at random are 1890 , 1230 , 2220 , and 1360 . We need to find Find the z-scores that correspond to each value and determine whether any of the values are unusual. Let's find out:
We know that Z score is given by : ( data - Mean ) / ( standard deviation )
Z score ( X = 1890 ):
⇒ [tex]Z = \dfrac{1890-1473}{318} = 1.31[/tex]
Z score ( X = 1230 ):
⇒ [tex]Z = \dfrac{1230-1473}{318} = -0.76[/tex]
Z score ( X = 2220 ):
⇒ [tex]Z = \dfrac{2220-1473}{318} = 2.34[/tex]
This value of Z is unusual as Value lies as : [tex]-2\leq Z\leq 2[/tex] .
Z score ( X = 1360 ):
⇒ [tex]Z = \dfrac{1360-1473}{318} = -0.35[/tex]