Important note: Before we use the normal distribution to compute probabilities, we must verify that the distribution of interest is very close to normal. The normal distribution may characterize either distributions of individual data points in a population of scores or the theoretical distribution of sample statistics such as the mean. The total area under the curve sums to 100%. Tails of a normal distribution are asymptotic, indefinitely decreasing but never touching the x-axis. Although normal distributions may have different means and standard deviations, all normal distributions are “bell-curve” shaped, symmetrical with the greatest height at the mean. The normal distribution is defined by a mathematical formula.
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