z Scores

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Z-Scores can be turned into percentages. Here's the deal - if you know a Z-Score - you know what percentage or proportion of scores are above and below that score. It's like slicing a pie. Cut it in quarters and you know that each quarter is 25% of the pie. Let's slice the normal curve. The distribution holds 100% of the scores or a proportion of 1.0

The gray line cuts it in half. So - half are below and half above. If you received the average score on the test (Z = 0.0), you did better than 50% of the class. What about cutting the distribution in another place? Calculus types have determined the percentages above and below any Z-Score. Your statistics book has a table with this information in it (Z-Table).