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Q: What properties distinguishes standard normal distribution from other normal distribution?

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The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.

0.368 or 36.8%.And you should specify that it is a standard normal distribution.0.368 or 36.8%.And you should specify that it is a standard normal distribution.0.368 or 36.8%.And you should specify that it is a standard normal distribution.0.368 or 36.8%.And you should specify that it is a standard normal distribution.

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.

It is a continuous distribution. Its domain is the positive real numbers. It is a member of the exponential family of distributions. It is characterised by one parameter. It has additive properties in terms of the defining parameter. Finally, although this is a property of the standard normal distribution, not the chi-square, it explains the importance of the chi-square distribution in hypothesis testing: If Z1, Z2, ..., Zn are n independent standard Normal variables, then the sum of their squares has a chi-square distribution with n degrees of freedom.

If a random variable X has a Normal distribution with mean m and standard deviation s, then z = (X - m)/s has a Standard Normal distribution. That is, Z has a Normal distribution with mean 0 and standard deviation 1. Probabilities for a general Normal distribution are extremely difficult to obtain but values for the Standard Normal have been calculated numerically and are widely tabulated. The z-transformation is, therefore, used to evaluate probabilities for Normally distributed random variables.

Related questions

The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.

The standard normal distribution has a mean of 0 and a standard deviation of 1.

The standard deviation in a standard normal distribution is 1.

The standard normal distribution is a normal distribution with mean 0 and variance 1.

The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.

The standard deviation in a standard normal distribution is 1.

The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.

A mathematical definition of a standard normal distribution is given in the related link. A standard normal distribution is a normal distribution with a mean of 0 and a variance of 1.

The mean of a standard normal distribution is 0.

Yes, the normal distribution, standard or not is always continuous.

The standard normal distribution is a special case normal distribution, which has a mean of zero and a standard deviation of one.

When its probability distribution the standard normal distribution.

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