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Why is the normal probability distribution widely used in practice?
Wiki User
∙ 10y ago
Suppose you have a random variable, X, with any distribution. Suppose you take a sample of n independent observations, X1, X2, ... Xn and calculate their mean. Repeat this process several times. Then as the sample size increases and the number of repeats increases, the distribution of the means tends towards a normal distribution. This is due to the Central Limit Theorem.
One consequence is that many common statistical measures have an approximately normal distribution.
Wiki User
∙ 10y ago
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Why normal distribution is better than other distributions?
It may not be better, but there is a lot of information on the normal distribution. It is one of the most widely used in statistics.
What is extensive distribution?
Making a product widely available..... Opposite to selective distribution.....associated with market penetration
What is the most important distribution in the galaxy and is widely used in all kinds of statistical inference?
The Gaussian distribution is the single most important distribution.
What does standard deviation tell about distribution?
How widely spread out, or tightly concentrated about the mean it is.
What is the history of exponential distribution?
Exponential DistributionThe exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.
Why you prefer normal distribution for other?
It is probably the most widely used distribution in statistics. In addition, a lot of information exists on this distribution.
Why is a bell curve used?
Bell curves are used because they represent an exactly normal distribution. A normal distribution means that all of the values are centered around a single mean value, with the probability density decreasing equally on either side of the mean. This is the distribution that is most widely used in statistics because it is often found naturally (truly random data follows a normal distribution), and also because it follows from the central limit theorem.
Why normal distribution is better than other distributions?
It may not be better, but there is a lot of information on the normal distribution. It is one of the most widely used in statistics.
What is the z value for a normal distribution?
If a random variable X has a Normal distribution with mean m and standard deviation s, then z = (X - m)/s has a Standard Normal distribution. That is, Z has a Normal distribution with mean 0 and standard deviation 1. Probabilities for a general Normal distribution are extremely difficult to obtain but values for the Standard Normal have been calculated numerically and are widely tabulated. The z-transformation is, therefore, used to evaluate probabilities for Normally distributed random variables.
How do you find the probability between two values given the population mean and standard deviation?
The answer depends on the distribution of the random variable. For some variables it is easy to calculate the cumulative distribution, F(x).Then, the probability between the values p and q is F(q) - F(p). WARNING: This might need minor modification if the the distribution is discrete.The normal distribution is one which, in general, cannot be evaluated analytically. However, you can convert p and q to the x=corresponding z-score. If m is the mean and s the standard deviations, then z1 = (p - m)/s and z2 = (q - m)/s. The cumulative probability function for Z is tabulated (widely available online) and the probability between p and q is F(z2) - F(z1).Note, however, that sometimes the tabulated values are (Prob - 0.5), or are 1 - Prob(z) so read notes to the table.
What is extensive distribution?
Making a product widely available..... Opposite to selective distribution.....associated with market penetration
What is the most important distribution in the galaxy and is widely used in all kinds of statistical inference?
The Gaussian distribution is the single most important distribution.
How do you find the probability density function?
The probability density function of a random variable can be either chosen from a group of widely used probability density functions (e.g.: normal, uniform, exponential), based on theoretical arguments, or estimated from the data (if you are observing data generated by a specific density function). More material on density functions can be found by following the links below.
What does standard deviation tell about distribution?
How widely spread out, or tightly concentrated about the mean it is.
What is the history of exponential distribution?
Exponential DistributionThe exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.
What do both variance and the standard deviaton tell you about distribution?
How widely spread out, or tightly concentrated about the mean the observations are.
What is the illiteracy population in Africa?
Leopards have the largest distribution of any wild cat, occurring widely in eastern and central Africa.
