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

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

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

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

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