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This is the diagram of a normal distribution
curve or z distribution. Note the bell shape of the curve and that its
ends/tail don’t touch the horizontal axis below. As I mentioned earlier, the
area under the curve equals 1 or 100%. Therefore, each half of the
distribution from the center (that is from the mean is equal to 50%. Thus,
the area from/above the mean up to 1 standard deviation is equal to 33.35%,
area above +1 standard deviation is equal to 13.6%, the area above +2
standard deviation is equal to 2.2% and area above +3 standard deviations is
equal to 0.1%. Since the other half is a mirror image, the
percentage/proportion of area above -1 standard deviation is the same as the
area above + 1 standard deviation i.e. it is 33.35%. And -2 standard
deviation=+2 standard deviation and so forth…. |