1. 8. Normal distribution Cambridge University Press  G K Powers 2013
Study guide Chapter 8

2. z-scores
z-score is the number of standard deviations the score is from the mean.
z – z-score or standardised score
x – Score
– Mean of a set of scores
s – Standard deviation (s = for population)
HSC Hint – Check your substitutions into the formula and whether your answer is reasonable.
Cambridge University Press
 G K Powers 2013

3. Using z-scores to compare data
Z-scores are used to compare scores from different data sets.
Read the question carefully to determine whether a higher or lower z-score is better.
The larger the z-score (ignoring the positive or negative) the further away it is from the centre of the data.
HSC Hint – Learn the meaning of a z-score. Use the z-score to compare scores from different sets of data.
Cambridge University Press
 G K Powers 2013

4. Properties of a normal distribution
Normally distributed data has the same mean, median and mode. It is symmetrical about the mean.
In a normal distribution:
68% of scores have a z-score between 1 and −1 (mostly in this range).
95% of scores have a z-score between 2 and −2 (very probably in this range)
99.7% of scores have a z-score between 3 and −3 (almost certainly in this range)
HSC Hint – Learn the percentages given above and their range of z-scores.
Cambridge University Press
 G K Powers 2013

5. Properties of a normal distribution
A bell-shaped curve represents a normal distribution. The z-scores on either side of the mean have the same percentage of the scores.
HSC Hint – Make sure you understand the symmetrical nature of normally distributed data.
Cambridge University Press
 G K Powers 2013