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What else can I help you with?
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.
True or false two normal distributions that have the same mean are centered at the same place regardless of the relationship between their standard deviation?
True. Two normal distributions that have the same mean are centered at the same point on the horizontal axis, regardless of their standard deviations. The standard deviation affects the spread or width of the distributions, but it does not change their center location. Therefore, even with different standard deviations, the distributions will overlap at the mean.
Why is it correct to say a normal disstrubtion and the standard normal distribution?
A normal distribution refers to a continuous probability distribution that is symmetrical and characterized by its mean and standard deviation. In contrast, the standard normal distribution is a specific case of the normal distribution where the mean is 0 and the standard deviation is 1. This standardization allows for easier comparison and calculation of probabilities using z-scores, which represent the number of standard deviations a data point is from the mean. Thus, while all standard normal distributions are normal, not all normal distributions are standard.
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.
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
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.
Is the standard deviation of standard normal distribution alway equal to 1?
Yes, the standard deviation of a standard normal distribution is always equal to 1. The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1, which allows it to serve as a reference for other normal distributions. This property is essential for standardizing scores and facilitating comparisons across different datasets.
