Question

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 . Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

Answer 1

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 ):

⇒ $Z = \dfrac{1890-1473}{318} = 1.31$

Z score ( X = 1230 ):

⇒ $Z = \dfrac{1230-1473}{318} = -0.76$

Z score ( X = 2220 ):

⇒ $Z = \dfrac{2220-1473}{318} = 2.34$

This value of Z is unusual as Value lies as : $-2\leq Z\leq 2$ .

Z score ( X = 1360 ):

⇒ $Z = \dfrac{1360-1473}{318} = -0.35$