Question

Given a distribution of scores with a mean of 40 and a standard deviation of 6, convert the following scores to the standard scores indicated:

a) X = 42 to a GRE score (a standard score with a mean of 500 and a standard deviation of 100)

b) X = 29 to an IQ score (a standard score with a mean of 100 and a standard deviation of 15)

Answer 1

Solution :

Given that ,

a) mean = = 40

standard deviation =  = 6

x = 42

Using z-score formula,

z = x - /   

z = 42 - 40 / 6

z = 0.33

= 500,   = 100

Using z-score formula,

x = z * +

x = 0.33 * 100 + 500

x = 533

b) mean = = 40

standard deviation =  = 6

x = 29

Using z-score formula,

z = x - /   

z = 29 - 40 / 6

z = -1.83

= 100,   = 15

Using z-score formula,

x = z * +

x = -1.83 * 15 + 100

x = 72.55