The Normal (or Gaussian) distribution is a symmetrical probability function whose shape is determined by two values: the mean and variance (or standard deviation).
According to the law of large numbers, if you take repeated independent samples from any distribution, the means of those samples are distributed approximately normally. The greater the size of each sample, or the greater the number of samples, the more closely the results will match the normal distribution. This characteristic makes the Normal distribution central to statistical theory.
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The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
The domain of the normal distribution is infinite.
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
No. Normal distribution is a special case of distribution.
The normal distribution can have any real number as mean and any positive number as variance. The mean of the standard normal distribution is 0 and its variance is 1.