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Is symmetrical a characteristic of a normal distribution?
The Normal ditribution is symmetric but so are other distributions.
Why you prefer normal distribution over other distributions in statistics?
we prefer normal distribution over other distribution in statistics because most of the data around us is continuous. So, for continuous data normal distribution is used.
Why Normal distribution is better then other distributions in statistics?
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.
Are all symmetric distributions normal distributions?
No. There are many other distributions, including discrete ones, that are symmetrical.
How to identify the the shape of probability distribution?
You cannot. There are hundreds of different distributions. The shapes of the distributions depend on their parameters so that the same distribution can be symmetric when the parameters have some specific value, but is highly skewed - in either direction - for other values.
