Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1474

and the standard deviation was 312. The test scores of four students selected at random are

1860,1230​, 2170​, and 1380.

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

a)z-score for 1860 is

b)z-score for 1230 is

c)z-score for 2170 is

d)z-score for 1380 is

which values if any are unusual ?

Answer 1

Solution :

z = (x - ) /

a)z-score for 1860 is

z = (1860 - 1474) / 312 = 1.24

b)z-score for 1230 is

z = (1230 - 1474) / 312 = -0.78

c)z-score for 2170 is

z = (2170 - 1474) / 312 = 2.23

d)z-score for 1380 is

z = (1380 - 1474) / 312 = -2.94

Values 2170 and 1380 are unusual