Question

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.

Answer #1

**Answer** :

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,**

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