Chapter ISG, Problem 10.5STP

To determine

To calculate z-score for each score and find test score for z-score -3 and 2.22.

Answer to Problem 10.5STP

Z-score for test score 70 is -0.5

Z-score for test score 80 is -0.5

Z-score for test score 84 is 1

Z-score for test score 90 is 1.6

Test score for z-score -3 is 48

Test score for z-score 2.22 is 95

Explanation of Solution

Given information:

Test scores 70, 80, 84, 90

z-score=-3

z-score=2.22

Mean=75

SD=9

Formula used:

  

  is mean

SD is standard deviation.

Calculation:

Z-score for test score 70

Using formula

  

On solving,

  

Z-score for test score 80

Using formula

  

On solving,

  

Z-score for test score 84

Using formula

  

On solving,

  

Z-score for test score 90

Using formula

  

On solving,

  

Test score for z-score -3

Using formula

  

Substituting value of z-score=-3 in above

  

On solving,

x=48

Test score for z-score 2.22

Using formula

  

Substituting value of z-score=2.22 in above

  

On solving,

x=95