In this article, the focus is on understanding the normal distribution, the associated empirical rule, its parameters and how to compute \(Z\) scores to find probabilities under the curve (illustrated with examples). For instance, given that adult height follows a normal distribution, most adults are close to the average height and extremely short adults occur as infrequently as extremely tall adults. Last but not least, since the normal distribution is symmetric around its mean, extreme values in both tails of the distribution are equivalently unlikely. In this sense, for a given variable, it is common to find values close to the mean, but less and less likely to find values as we move away from the mean. Moreover, the further a measure deviates from the mean, the lower the probability of occurring. The normal distribution is a mount-shaped, unimodal and symmetric distribution where most measurements gather around the mean. Many natural phenomena in real life can be approximated by a bell-shaped frequency distribution known as the normal distribution or the Gaussian distribution. The normal distribution is a function that defines how a set of measurements is distributed around the center of these measurements (i.e., the mean).
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