The importance of normal distributions is primarily due to the fact that the distributions of many natural phenomena are at least roughly normally distributed. One of the fist applications of normal distributions was the analysis of errors of measurements made in astronomical observations, errors caused by imperfect instruments and imperfect observers. Galileo noted int he seven-teeth century that these errors were symmetrical and that small errors occurred more frequently than large ones.
This led to several hypothetical distributions of errors, but it was not until the early 19th century that it was discovered that these errors followed a normal distribution. Independently, the mathematicians Adrain in 1808 and Gauss in 1809 developed a formula for the normal distribution and showed that errors are aligned with this distribution.