Question

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

1. A score that is 20 points above the mean.
2. A score that is 10 points below the mean.
3. A score that is 15 points above the mean
4. A score that is 30 points below the mean.

Answer 1

Z = ( X - ) /

a)

Given, ( X - ) = 20 (above the mean)

z = 20 / 10

= 2

b)

( X - ) = -10 (below the mean)

z = -10 / 10

= -1

c)

( X - ) = 15 (above the mean)

z = 15 / 10

=  1.5

d)

( X - ) = -30 (Below the mean)

z = -30 / 10

= -3