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

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 = (1890-1473)/(318) = 1.31`

Z score ( X = 1230 ):

⇒
`Z = (1230-1473)/(318) = -0.76`

Z score ( X = 2220 ):

⇒
`Z = (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 = (1360-1473)/(318) = -0.35`