It can do. If you define a quarter of it as one part and the rest as another, the two WILL be different! But the distribution IS symmetric about its mean.
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No, they are two very different distributions.
A normal distribution is defined by two parameters: the mean, m, and the variance s2, (or standard deviation, s).The standard normal distribution is the special case of the normal distribution in which m = 0 and s = 1.
There is no such thing. The Normal (or Gaussian) and Binomial are two distributions.
The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.
The Cauchy or Cauchy-Lorentz distribution. The ratio of two Normal random variables has a C-L distribution.