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Do normal probability distributions have different arithmetic means and different standard deviations?
Yes. And that is true of most probability distributions.
What is the benefit of transforming standard normal distributions to conform to the standard distribution?
There are no benefits in doing something that cannot be done. The standard normal distribution is not transformed to the standard distribution because the latter does not exist.
Do some normal probability distributions have different means and different standard deviations?
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.
Do some normal probability distributions have different arithmetic means and different standard deviations?
Yes. Most do.
Why normality is required for standard deviation application?
Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.
Do normal probability distributions have different arithmetic means and different standard deviations?
Yes. And that is true of most probability distributions.
How does one interpret a standard deviation which is more than the mean?
Standard deviation is a measure of the dispersion of the data. When the standard deviation is greater than the mean, a coefficient of variation is greater than one. See: http://en.wikipedia.org/wiki/Coefficient_of_variation If you assume the data is normally distributed, then the lower limit of the interval of the mean +/- one standard deviation (68% confidence interval) will be a negative value. If it is not realistic to have negative values, then the assumption of a normal distribution may be in error and you should consider other distributions. Common distributions with no negative values are gamma, log normal and exponential.
What is standard normal variate?
It's the same as a z-Transformation. for all xi: (xi-mean(x)) / std(x)
What is the benefit of transforming standard normal distributions to conform to the standard distribution?
There are no benefits in doing something that cannot be done. The standard normal distribution is not transformed to the standard distribution because the latter does not exist.
Do some normal probability distributions have different means and different standard deviations?
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.
Do some normal probability distributions have different arithmetic means and different standard deviations?
Yes. Most do.
Why is a chi-squared test for qualitative data always right-tailed?
A chi square is square of standard normal variate, so all values are positive
In what ways is the t distribution similar to the standard normal distribution?
Check the lecture on t distributions at StatLect. It is explained there.
Why standard deviation is best measure of dispersion?
standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.
How many standard normal distributions are there?
Only one. A normal, or Gaussian distribution is completely defined by its mean and variance. The standard normal has mean = 0 and variance = 1. There is no other parameter, so no other source of variability.
Why normality is required for standard deviation application?
Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.
Are all symmetric distributions normal distributions?
No. There are many other distributions, including discrete ones, that are symmetrical.
