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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.
Does this means that all symmetric distribution are normal Explain?
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.
What role do z-scores play in the transformation of data from multiple distributions to the standard normal distribution?
None.z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.
When referring to the normal probability there is not just one there is a family of distributions?
A family that is defined by two parameters: the mean and variance (or standard deviation).
Can the standard normal variate in normal distributions be negative?
About half the time.
Do normal probability distributions have different arithmetic means and different standard deviations?
Yes. And that is true of most probability distributions.
Are all symmetric distributions normal distributions?
No. There are many other distributions, including discrete ones, that are symmetrical.
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.
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.
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.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
Does this means that all symmetric distribution are normal Explain?
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.
What role do z-scores play in the transformation of data from multiple distributions to the standard normal distribution?
None.z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.
