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Just a note
In this case we have chosen a value of x equal to the population mean  where the slope is at its steepest. Moreover, because this distribution is symmetrical, the median is the same as the median  the value of x where P = 0.5. If we randomly select an observation from any distribution, it is equally likely to be above the population's median or below that median  but, because the normal distribution is symmetrical, this rule also applies to the population's mean.
Because the cumulative function integrates (assembles) all the relative frequencies of X to the left of x, P is equivalent to the area under to curve (above) to the left of x. Nevertheless, the total area under this curve (where x is infinite) must always equal one.
