Chapter 4: Analysing the Data |

## The standard normal distributionAny distribution can be converted to a standardised distribution. However the symmetry of the original distribution remains unchanged. If the original distribution was skewed to start with, it will still be skewed after the z-score transformation. In the special case where the Importantly, the percent (or proportion) of scores falling above or below any Z-score is known and tabled (in Howell, see Appendix Z, p. 695). So, consider the following example. Suppose the distribution of final exam marks in PESS202 is roughly normally distribution with a mean of 68 and a standard deviation of 10. What percent of students score above 73? To answer this question, you need to express 73 as a Z-score. Using the procedure already described, the Z-score is 0.5. In other words, 73 is one half of a standard deviation above the mean. So we want to know what percent of the scores are above one half of a standard deviation (that is, with a Z-score greater than 0.5). By using the table in Appendix Z of Howell, we see that the proportion of scores above a Z of 0.5 is .3085 if the distribution is normal. So expressed as a percentage, 30.85% or about 31% of students score above 73. Using the same procedure described earlier and a standard normal table, it is possible to entertain questions about percentages or proportions of scores greater than, less than, or between any score or set of scores. |

© Copyright 2000 University of New England, Armidale, NSW, 2351. All rights reserved Maintained by Dr Ian Price |