Many variables are nearly normal, but none are exactly normal. Thus the normal distribution, while not perfect for any single problem, is very useful for a variety of problems. We will use it in data exploration and to solve important problems in statistics. Every normal distribution is a version of the standard normal distribution that's been stretched or squeezed and moved horizontally right or left. The mean determines where the curve is centered. Increasing the mean moves the curve right, while decreasing it moves the curve left. The standard deviation stretches or squeezes the curve.
The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean.
Normal Distributions. The normal distribution is the most important and most widely used distribution in statistics. It is sometimes called the "bell curve," although the tonal qualities of such a bell would be less than pleasing. It is also called the "Gaussian curve" of Gaussian distribution after the mathematician Karl Friedrich Gauss.
The normal distribution is a theoretical distribution of values for a population and has a precise mathematical definition. Data values that are a sample from a normal distribution are said to be "normally distributed."
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what is normal distribution used for