Normal distribution intuition

Many real data sets cluster into a normal distribution, a symmetric bell-shaped curve centered on the mean; knowing the mean and standard deviation lets you estimate what percentage of the data falls in a given range, using the area under that part of the curve. For example, if adult heights have a mean of 65 inches and a standard deviation of 3 inches, then 65 - 3 = 62 and 65 + 3 = 68, and about 68% of people fall in that range, one standard deviation from the mean, though not every data set is actually shaped like this.

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