Question

The intelligence quotient (IQ) score, as measured by the Stanford-Binet IQ test, is normally distributed in a certain population of children. The mean IQ score is 96 points, and the standard deviation is 15.72 points. Convert the following into z-scores:

a) x = 117


b) x = 132


c) x = 92


c) x = 72

Answer 1

Z score calculates how many standard deviation above or below the mean , a raw score is.

where x is the raw score, is the mean and is the standard deviation of sample.

a) (117 -96) / 15.72

= 1.33

117 is 1.33 standard deviations above the mean.

b) ( 132 -96)/ 15.72

= 2.29

132 is 2.29 deviations above the mean.

c) ( 92 - 96) / 15.72

- 0.25

92 is 0.25 deviations below the mean.

d) ( 72 - 96) / 15.72

= -1.52

72 is 1.52 deviations below the mean