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The Standard Normal Distribution and Z-scores
Home Introducing the Normal Distribution The Normal Distribution and Z-scores The Standard Normal Distribution and Z-scores Finding Probabilities Associated with a Z-score Why do you need a table to find probabilities with z-scores? Above, Below and Between Probabilities Converting Percentages to Z-scoresView All Tutorials
 Why do you need a table to find probabilities with z-scores?
Fundamentals of Statistics 2: The Normal Distribution :: Finding Probabilities Associated with a Z-score
An 6 foot tall adult male is .5 standard deviations taller than the average North American male (a z-score of .5). To find the probability associated with this z-score we lookup .5 in a table of normal probabilities or use the online calculator. We get the cumulative area of .6915, meaning being 6'0 puts you in the 69th percentile of heights, or you're taller than 69% of adult males in North America and shorter than about 31%. 



Below is a small example of a table of normal probabilities. What you want to do is find the z-score that matches as close as possible to the one you have, then look for the area up to this point.




 z Larger Portion
Smaller Portion
 0.45  .6736  .3264
 0.46  .6772  .3228
 0.47  .6808  .3192
 0.48  .6844  .3156
 0.49  .6879  .3121
 0.50  .6915  .3085
 0.51  .6950  .3050
 0.52
  .6985  .3015
 0.53  .7019  .2981
 0.54  .7054  .2946
 0.55  .7088  .2912
 0.56  .7123  .2877
 0.57  .7157  .2843



I've put together an excel calculator which will do almost anything you want to do with z-scores. You can watch a short-overview of that below.


 
The Standard Normal Distribution and Z-scores
Home Introducing the Normal Distribution The Normal Distribution and Z-scores The Standard Normal Distribution and Z-scores Finding Probabilities Associated with a Z-score Why do you need a table to find probabilities with z-scores? Above, Below and Between Probabilities Converting Percentages to Z-scoresView All Tutorials
 Why do you need a table to find probabilities with z-scores?

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