George E.P. Box (1979) on statistical modelling:
|All models are wrong, but some are useful.|
The normal distribution probability density function is defined over all real x, so in principle it cannot be a correct model for the distribution of nonnegative variables such as height, weight, etc. The fact that it is in use and helps us solve practical problems (such as providing a quantitative basis for detecting over and underweight people) is a testament to Box’s insight.