Symmetric Versus Skewed A probability distribution can be symmetric or skewed to the left or right. You typically choose between a symmetric and skewed distribution on the basis of realism. For example, if you want to model a student’s score on a 100-point exam, you will probably choose a left-skewed distribution. This is because a few poorly prepared students typically “pull down the curve.” On the other hand, if you want to model the time it takes to serve a customer at a bank, you will probably choose a right-skewed distribution. This is because most customers take only a minute or two, but a few customers take a long time. Finally, if you want to model the monthly return on a stock, you might choose a distribution symmetric around zero, reasoning that
The heights above a density function are not probabilities, but they still indicate relative likelihoods of the possible values.
the stock return is just as likely to be positive as negative and there is no obvious reason for skewness in either direction.
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