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Q: Is the uniform probability distribution's standard deviation proportional to the distribution's range?
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Is variance directly proportional to standard deviation?

Variance isn't directly proportional to standard deviation.

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).

Do normal probability distributions have different arithmetic means and different standard deviations?

Yes. And that is true of most probability distributions.

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 do the variance and the standard deviation measure?

They are measures of the spread of distributions about their mean.

How do you find highest standard deviation in given number?

Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.

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.

What is Normal of Standard Normal Probability Distribution?

with mean of and standard deviation of 1.

How do you calculate probability given mean and standard deviation?

The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question.

Why is the standard normal probability distribution unique?

a mean of 1 and any standard deviation

What is Normal of probability distribution?

with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.

What does is mean when the standard deviation is 0?

Intuitively, a standard deviation is a change from the expected value.For the question you asked, this means that the change in the "results" doesn't exist, which doesn't really happen. If the standard deviation is 0, then it's impossible to perform the test! This shows that it's impossible to compute the probability with the "null" standard deviation from this form:z = (x - µ)/σIf σ = 0, then the probability doesn't exist.