Question

For each of the following, would a score of X = 85 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? µ =75 and σ = 15 µ =80 and σ = 2 µ =90 and σ = 20 µ =93 and σ = 3

Answer 1

Solution :

Given that ,

x = 85

a) mean = = 75

standard deviation =  = 15

Using z-score formula,

z = x - /   

z = 85 - 75 / 15

z = 0.67

central score

b) mean = = 80

standard deviation =  = 2

Using z-score formula,

z = x - /   

z = 85 - 80 / 2

z = 2.50

extreme score

c) mean = = 90

standard deviation =  = 20

Using z-score formula,

z = x - /   

z = 85 - 90 / 20

z = -0.25

central score

d) mean = = 93

standard deviation =  = 3

Using z-score formula,

z = x - /   

z = 85 - 93 / 3

z = -2.67

extreme score