# Distribution

A normal distribution or “bell curve” is a representation of the results we see in given situations. Bell curves can be used to portray data used in everyday life, such as test scores, salaries, even blood pressure. In any case, the majority of results will yield the “average”, while fewer will be slightly below or above average, and ever fewer will be the highest and lowest values under the curve. A standard normal distribution is the most commonly used normal distribution with a mean of 1 and a standard deviation of 1. In the standard normal distribution, 68% of data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations of the mean. Look at the bell curve below: [Image 6: Standard normal distribution curve. Source: University of North Carolina, 2009.]

In all normal distributions, the area under the curve is 1, the curve is symmetrical around the mean, and exactly half of the data falls on the right and left of the mean.

Example: If students in a math class took a final exam, 68% of students would score mostly C’s; 95% of students would score mostly C’s, some B’s and some D’s; and 99.7% of students would score mostly C’s, some B’s and D’s, and ever fewer A’s and F’s.

 Freeman and Company “Sampling Distributions for Counts and Proportions.” UNC, 2009. Web.

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