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. Recognize and use the standard normal probability distribution. A special continuous distribution, called normal, is the most common and therefore most important of all the distributions. It is widely used and even more widely abused. Its graph is bell-shaped. You see the bell curve in almost all disciplines. 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. The Normal Distribution is used to analyze data when there is an equal chance for the data to be above and below the average value of the continuous data. It is named after the famous mathematician and physicist Carl Friedrich Gauss. The 5 common properties of Normal Distribution are: Normal Distribution Curve is symmetric about the mean. A normal distribution is significant in statistics and is often used in the natural sciences and social arts to describe real-valued random variables whose distributions are unknown. Q4 What are the characteristics of a normal distribution? .

what is normal distribution used for