what is a normal distribution 
normal distribution also known as the gaussian distribution is a probability distribution that is symmetric about the mean showing that data near the mean are more frequent in occurrence than data far from the mean the normal distribution appears as a bell curve when graphed investopedia lara antalproperties of normal distributionthe normal distribution is the most common type of distribution assumed in technical stock market analysis the standard normal distribution has two parameters the mean and the standard deviation in a normal distribution mean average median midpoint and mode most frequent observation are equal these values represent the peak or highest point the distribution then falls symmetrically around the mean the width of which is defined by the standard deviation the normal distribution model is key to the central limit theorem clt which states that averages calculated from independent identically distributed random variables have approximately normal distributions regardless of the type of distribution from which the variables are sampled 1the normal distribution is one type of symmetrical distribution symmetrical distributions occur when a dividing line produces two mirror images not all symmetrical distributions are normal since some data could appear as two humps or a series of hills in addition to the bell curve that indicates a normal distribution observationsfor all normal distributions 68 2 of the observations will appear within plus or minus one standard deviation of the mean 95 4 will fall within two standard deviations and 99 7 within three standard deviations this fact is sometimes called the empirical rule a heuristic that describes where most of the data in a normal distribution will appear data falling outside three standard deviations 3 sigma would signify rare occurrences investopedia sabrina jiangskewness measures the degree of symmetry of a distribution the normal distribution is symmetric and has a skewness of zero if the distribution of a data set instead has a skewness less than zero or negative skewness left skewness then the left tail of the distribution is longer than the right tail positive skewness right skewness implies that the right tail of the distribution is longer than the left kurtosis measures the thickness of the tail ends of a distribution to the tails of a distribution the normal distribution has a kurtosis equal to 3 0 distributions with larger kurtosis greater than 3 0 exhibit tail data exceeding the tails of the normal distribution e g five or more standard deviations from the mean this excess kurtosis is known in statistics as leptokurtic but is more colloquially known as fat tails the occurrence of fat tails in financial markets describes what is known as tail risk distributions with low kurtosis less than 3 0 platykurtic exhibit tails that are generally less extreme skinnier than the tails of the normal distribution formulathe normal distribution follows the following formula note that only the values of the mean and standard deviation are necessary