Question

1. In a distribution m= 80 and sigma = 20.  

a) What are the standard scores (z scores) for each of the following?

            10, 6, 70, 90, 73

2. For the same distribution what are the scores associated with the following z scores?

            Z= + 1.0, Z = 0, Z= +1.5, Z= -2

Answer 1

Given that, mean = 80 and standard deviation = 20

a) We want to find the standard scores ( z scores) for the following scores,

i) x = 10

z score = -3.5

ii) x = 6

z score = -3.7

iii) x = 70

z score = -0.5

iv) x = 90

z score = 0.5

v) x = 73

z score = -0.35

b) We want to find, the scores associated with the following z scores,

i) Z = +1.0

Raw score = 100

ii) Z = 0

Raw score = 80

iii) Z = +1.5

Raw score = 110

iv) Z = -2

Raw score = 40