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

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Variance isn't directly proportional to 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.

The probability of scoring an exact value for a continuous variable is zero for any value. The probability of scoring 115 (or more) is 15.87%

The Normal distribution is a probability distribution of the exponential family. It is a symmetric distribution which is defined by just two parameters: its mean and variance (or standard deviation. It is one of the most commonly occurring distributions for continuous variables. Also, under suitable conditions, other distributions can be approximated by the Normal. Unfortunately, these approximations are often used even if the required conditions are not met!

Information is not sufficient to find mean deviation and standard deviation.

Related questions

Variance isn't directly proportional to standard deviation.

A family that is defined by two parameters: the mean and variance (or standard deviation).

Yes. And that is true of most probability distributions.

Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.

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

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

standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.

with mean of and standard deviation of 1.

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.

a mean of 1 and any standard deviation

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

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 - Âµ)/ÏƒIf Ïƒ = 0, then the probability doesn't exist.