What probability does is assign a value (the probability) to a particular outcome. The rest of this answer is a somewhat lengthy explanation, but I couldn't think of a way to shorten it without sacrificing a point. In fact, that is how we define impossible. The shortest answer would be: having a probability of zero is equivalent with being impossible. This is a good question about probability. For more information on the nature of the normal distribution, take a look at At last, the exponential gives the function its asymptotic behavior. The variable squared gives this function is parabolic look, while the negative sign makes its concavity look downward. So the core of the normal distribution is exp(-x²/2). f(x/2) is tighter, while f(x/0.5) is wider than the original f(x). Finally, if you try out exp(-((x-mu)/sigma)²/2) you'll then find out that you have the same shape shifted by the mean and elongated or shrunk by the standard deviation. That is a basic characteristic of the normal distribution. If you then graph exp(-(x-mu)²/2), you'll see the same function shifted by its mean - the mean must correspond to the function's maximum. If you try to graph that, you'll see it looks already like the bell shape of the normal function. Actually, the normal distribution is based on the function exp(-x²/2). So it must be normalized (integral of negative to positive infinity must be equal to 1 in order to define a probability density distribution). The integral of the rest of the function is square root of 2xpi.
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