Question

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

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1540 and the standard deviation was 314.

The test scores of four students selected at random are 1970​, 1290​, 2270​, and 1430.

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

Given data is :

Mean = = 1540

Standard deviation = = 314

and,test scores of 4 students selected at random are 1970​, 1290​, 2270​, and 1430.

First consider the test score for 1970 is :

i.e X = 1970

then

Z = (1970 - 1540) / 314

= 430 / 314

= 1.37

Z = 1.37

Now consider the test score for 1290 is :

i.e X = 1970

then

Z = (1290 - 1540) / 314

= -250 / 314

= -0.80

Z = -0.80

Now consider the test score for 2270 is :

i.e X = 2270

then

Z = (2270 - 1540) / 314

= 730 / 314

= 2.33

Z = 2.33

Now consider the test score for 1430 is :

i.e X = 1430

then

Z = (1430 - 1540) / 314

= -110 / 314

= -0.35

Z = -0.35

Based on these values there is no unusual z value here,