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.

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. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. 7.6: Normal Approximation to the Binomial. In the section on the history of the normal distribution, we saw that the normal distribution can be used to approximate the binomial distribution.
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.
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    • what is normal distribution used for