<P> I can only recognize the occurrence of the normal curve--the Laplacian curve of errors--as a very abnormal phenomenon . It is roughly approximated to in certain distributions; for this reason, and on account for its beautiful simplicity, we may, perhaps, use it as a first approximation, particularly in theoretical investigations . </P> <P> There are statistical methods to empirically test that assumption, see the above Normality tests section . </P> <Ul> <Li> In biology, the logarithm of various variables tend to have a normal distribution, that is, they tend to have a log - normal distribution (after separation on male / female subpopulations), with examples including: <Ul> <Li> Measures of size of living tissue (length, height, skin area, weight); </Li> <Li> The length of inert appendages (hair, claws, nails, teeth) of biological specimens, in the direction of growth; presumably the thickness of tree bark also falls under this category; </Li> <Li> Certain physiological measurements, such as blood pressure of adult humans . </Li> </Ul> </Li> <Li> In finance, in particular the Black--Scholes model, changes in the logarithm of exchange rates, price indices, and stock market indices are assumed normal (these variables behave like compound interest, not like simple interest, and so are multiplicative). Some mathematicians such as Benoit Mandelbrot have argued that log - Levy distributions, which possesses heavy tails would be a more appropriate model, in particular for the analysis for stock market crashes . The use of the assumption of normal distribution occurring in financial models has also been criticized by Nassim Nicholas Taleb in his works . </Li> <Li> Measurement errors in physical experiments are often modeled by a normal distribution . This use of a normal distribution does not imply that one is assuming the measurement errors are normally distributed, rather using the normal distribution produces the most conservative predictions possible given only knowledge about the mean and variance of the errors . </Li> <Li> In standardized testing, results can be made to have a normal distribution by either selecting the number and difficulty of questions (as in the IQ test) or transforming the raw test scores into "output" scores by fitting them to the normal distribution . For example, the SAT's traditional range of 200--800 is based on a normal distribution with a mean of 500 and a standard deviation of 100 . </Li> </Ul> <Li> In biology, the logarithm of various variables tend to have a normal distribution, that is, they tend to have a log - normal distribution (after separation on male / female subpopulations), with examples including: <Ul> <Li> Measures of size of living tissue (length, height, skin area, weight); </Li> <Li> The length of inert appendages (hair, claws, nails, teeth) of biological specimens, in the direction of growth; presumably the thickness of tree bark also falls under this category; </Li> <Li> Certain physiological measurements, such as blood pressure of adult humans . </Li> </Ul> </Li>

What is the mean of a bell curve