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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!
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What is the difference of a normal distribution and a stardard normal distribution?
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
What percent falls below the mean for normal distribution?
In a normal distribution half (50%) of the distribution falls below (to the left of) the mean.
What properties distinguishes standard normal distribution from other normal 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.
What is the expected shape of the distribution of the sample mean?
The distribution of the sample mean is bell-shaped or is a normal distribution.
What does a negative kurtosis mean?
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.
