Question

In each situation below, calculate the standardized score (or z-score) for the value x.

(a) Mean μ = 0, standard deviation σ = 1, value x = 1.5.

(b) Mean μ = 11, standard deviation σ = 7, value x = 4.

(c) Mean μ = 15, standard deviation σ = 5, value x = 0.

(d) Mean μ = -10, standard deviation σ = 10, value x = -30.

Answer 1

Solution :

Given that ,

a) mean = = 0

standard deviation =  = 1

x = 1.5

Using z-score formula,

z = x - /   

z = 1.5 - 0 / 1

z = 1.5

b) mean = = 11

standard deviation =  = 7

x = 4

Using z-score formula,

z = x - /   

z = 4 - 11 / 7

z = -1.0

c) mean = = 15

standard deviation =  = 5

x = 0

Using z-score formula,

z = x - /   

z = 0 - 15 / 5

z = -3.0

d) mean = = -10

standard deviation =  = 10

x = -30

Using z-score formula,

z = x - /   

z = -30 - (-10) / 10

z = -2.0