Question

Calculate the standard score (Z-Score) and indicate where the Z-Score would be on a Standard Normal Distribution (draw the normal distribution)

μ = 85 and σ = 15; x = 110

μ = 120 and σ = 12.5; x = 80

μ = 100 and σ = 20; x = 118

Answer 1

Solution :

Given that,

a ) mean = = 85

standard deviation = = 15

x = 110

Using z-score formula,

Z = ( x - / )

= ( 110 - 85 / 15 )

= 25 /15

= 1.666

Z-Score = 1.67

b ) mean = = 120

standard deviation = = 12.5

x = 80

Using z-score formula,

Z = ( x - / )

= ( 80 - 120 /12.5 )

= - 40 /12.5

= - 3.2

Z-Score = -3.2

c ) mean = = 100

standard deviation = = 20

x = 118

Using z-score formula,

Z = ( x - / )

= ( 100 - 118 / 20 )

= -18 /20

= -0.9

Z-Score = -0.9