Q: What is underlying distribution?

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If the underlying distribution of the product is normally distributed then (and only then) the normal distribution can be used to identify specimens that are outside the acceptable range.

The standard error of the underlying distribution, the method of selecting the sample from which the mean is derived, the size of the sample.

The answer depends on the underlying distribution. For example, if you have a random variable X, with a symmetric distribution with mean = 20 and sd = 1, then prob(X > 1) = 1, to at least 10 decimal places.

A large sample reduces the variability of the estimate. The extent to which variability is reduced depends on the quality of the sample, what variable is being estimated and the underlying distribution for that variable.

The Normal or Gaussian distribution is a probability distribution which depends on two parameters: the mean and the variance (or standard deviation). In may real life situations measurements are found to be approximately normal. Furthermore, even if the underlying distribution of a variable is not normal, the mean of a number of repeated observations of the variable will approximate the normal distribution.The term "approximate" is important because, although the heights of adult males (for example) appear to be normally distributed, the true normal distribution must allow negative heights whereas that is not physically possible!

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The answer depends on the underlying distribution.

The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.

It means independent of the underlying distribution.

The answer depends on the underlying distribution. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.Furthermore, if the distribution is continuous, the probability of any specific value is 0.The answer depends on the underlying distribution. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.Furthermore, if the distribution is continuous, the probability of any specific value is 0.The answer depends on the underlying distribution. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.Furthermore, if the distribution is continuous, the probability of any specific value is 0.The answer depends on the underlying distribution. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.Furthermore, if the distribution is continuous, the probability of any specific value is 0.

If the underlying distribution of the product is normally distributed then (and only then) the normal distribution can be used to identify specimens that are outside the acceptable range.

This is the Central Limit Theorem.

They tell you that the underlying distribution is very erratic.

It depends on the underlying distribution.

No. If the underlying distribution is approximately Normal then 1.4 is not at all unusual.

Because very many variables tend to have the Gaussian distribution. Furthermore, even if the underlying distribution is non-Gaussian, the distribution of the means of repeated samples will be Gaussian. As a result, the Gaussian distributions are also referred to as Normal.

The parameters of the underlying distribution, plus the standard error of observation.

According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.