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The normal distribution can have any real number as mean and any positive number as variance. The mean of the standard normal distribution is 0 and its variance is 1.

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Q: What properties distinguishes standard normal distribution from other normal distribution?
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What is the difference of a normal distribution and a stardard normal distribution?

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


What proportion of a normal distribution is located between z-0.90 and z 0.90?

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.


Why does a researcher want to go from a normal distribution to 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.


Properties of Chi-square distribution?

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.


What is the z value for a normal distribution?

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

What is the perfect standard normal distribution?

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.


How does standard normal distribution differ from normal distribution?

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


What is the standard deviation of a standard normal distribution?

The standard deviation in a standard normal distribution is 1.


What is the difference between a normal distribution and the standard normal distribution?

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


Which normal distribution is also the standard normal curve?

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


In the standard normal distribution the standard deviation is always what?

The standard deviation in a standard normal distribution is 1.


What is the difference of a normal distribution and a stardard normal distribution?

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


Carefully define a standard normal distribution?

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?

The mean of a standard normal distribution is 0.


Is the standard normal distribution is continuous?

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


In your own words describe the standard normal distribution?

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


When can you say the distribution is considered normal?

When its probability distribution the standard normal distribution.

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