Explain why that is possible. We define probabilities for various normal distributions. However, we use one single table (Standard Normal Distribution Table) for all of them.

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First, we convert all data to a standardized z-value, which basically is the number of standard deviations a given value is from the mean.

Now the graphs of different normal distributions can look "different"; some are very skinny, some broad, etc... But the similarities are what we are interested in. In each case, the area under the curve is exactly 1. The shape of the curve depends solely on the standard deviation (the mean shifts the curve along the horizontal axis). Since we are measuring the number of standard deviations a value is from the mean, the area remains the same.

For example, no matter what normal curve you are using, approximately 68% of the data lies within 1 standard deviation of the mean.

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