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Fundamentals of Statistics 2: The Normal Distribution :: Finding Probabilities Associated with a Zscore
An 6 foot tall adult male is .5 standard deviations taller than the average North American male (
a zscore of .5
). To find the probability associated with this zscore 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 zscore 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 zscores. You can watch a shortoverview of that below.
View All Tutorials
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