A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance.
A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
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The form of this question incorportates a false premise. The premise is that the data are normally distributed. Actually, is the sample mean which, under certain circumstances, is normally distributed.
No, but the approximation is better for normally distributed variables.
True.
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