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." 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 probability distribution, so the total area under the curve is always 1 or 100%. The formula for the normal probability density function looks fairly complicated. But to use it, you only need to know the population mean and standard deviation. 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. 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. 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. Normal distributions review. Google Classroom. Normal distributions come up time and time again in statistics. A normal distribution has some interesting properties: it has a bell shape, the mean and median are equal, and 68% of the data falls within 1 standard deviation. 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? 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. XTqrw.