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It is a consequence of the Central Limit Theorem (CLT).
Suppose you have a large number of independent random variables. Then, provided some fairly simple conditions are met, the CLT states that their mean has a distribution which approximates the Normal distribution - the bell curve.
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What is the standard deviation of the mean of 9.65?
It depends on what the distribution is. In a Normal or Gaussian distribution, the standard deviation is the square root of the mean, so it could be 3.1 but, again, it depends on the distribution.
Why you prefer normal distribution over other distributions in statistics?
we prefer normal distribution over other distribution in statistics because most of the data around us is continuous. So, for continuous data normal distribution is used.
What are the advantages of using standard normal distribution over the normal distribution?
The standard normal distribution is tabulated. The critical values for various outcomes can therefore be worked out easily from tables. The normal distribution is extremely difficult to integrate: most people, even with a university degree in mathematics will be unable to do so. So working out the probability of events from the normal distribution is near enough impossible.
What is the perfect standard normal distribution?
The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
What does probalility distribution mean?
In parametric statistical analysis we always have some probability distributions such as Normal, Binomial, Poisson uniform etc.In statistics we always work with data. So Probability distribution means "from which distribution the data are?
