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This is probably the most useful and widely used continuous probability distribution. The pdf is the familiar "bell-curve" and is given by
 
 

The picture alongside illustrates the Normal p.d.f.: 
 

The pdf has two parameters m (which is the mean of the distribution and specifies its location) and s (which is the SD and describes its spread). The various shapes shown alongside correspond to different Normal distributions with m  specifying where it is "centered" and s  specifying the spread around the center (small s means a "skinny" curve while a larger s means a curve that is more "spread out").

It may be shown that E[X]=m and V(X)=s².
Now suppose we want to find P(a£X£b). Clearly, trying to compute the value of is not desirable!
Instead we first make a transformation by defining Z = (X-m)/s

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Previous: Uniform Distribution