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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.