Question

1. A normal distribution of scores has a standard deviation of 10.  Find the z-scores corresponding to each of the following values:

a. A score that is 20 points above the mean.  

b. A score that is 10 points below the mean.

c. A score that is 15 points above the mean.

d. A score that is 30 points below the mean.  

Answer 1

Solution :

Given that ,

mean = = 0

standard deviation =  = 10

a) x = 20 ( above the mean)

Using z-score formula,

z = x - /   

z = 20 - 0 / 10

z = 2.00

b) x = -10 ( below the mean)

Using z-score formula,

z = x - /   

z = -10 - 0 / 10

z = -1.00

c) x = 15 ( above the mean)

Using z-score formula,

z = x - /   

z = 15 - 0 / 10

z = 1.50

d) x = -30 ( below the mean)

Using z-score formula,

z = x - /   

z = -30 - 0 / 10

z = -3.00