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Q: Does all symmetrical distributions are normal distribution?

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No. Normal distribution is a special case of distribution.

No. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.

use this link http://www.ltcconline.net/greenl/Courses/201/probdist/zScore.htm Say you start with 1000 observations from a standard normal distribution. Then the mean is 0 and the standard deviation is 1, ignoring sample error. If you multiply every observation by Beta and add Alpha, then the new results will have a mean of Alpha and a standard deviation of Beta. Or, do the reverse. Start with a normal distribution with mean Alpha and standard deviation Beta. Subtract Alpha from all observations and divide by Beta and you wind up with the standard normal distribution.

s= bracket n over sigma i (xi-x-)^2 all over n-1 closed bracket ^ 1/2

Related questions

No. There are many symmetrical distributions that are not Normal. A simple one is the uniform distribution:

No, not all distributions are symmetrical, and not all distributions have a single peak.

No. There are many other distributions, including discrete ones, that are symmetrical.

No. Normal distribution is a special case of distribution.

Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.

No. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

A normal distribution is symmetrical; the mean, median and mode are all the same, on the line of symmetry (middle) of the graph.

It is equal to zero in ALL distributions.

Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.

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.

standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.

Symmetrical. See http://www.orbitals.com for pictures of all the orbitals

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