A normal distribution is a continuous probability distribution that has a bell-shaped curve. Its mean and standard deviation define it. The mean is the average value of the data, and the standard deviation measures how to spread out the data (Zucchi, 2019). The normal distribution is symmetrical, meaning that the curve's left half mirrors the right half.
Normal Distribution in Construction:
In the construction field, many variables could result in a normal distribution. I will choose the height of buildings in a particular neighborhood; these variables are all continuous variables, meaning they can take on any value within a specific range. They are also all likely to be normally distributed, meaning that most values will be clustered around the mean, with fewer and fewer values as you move further away from the mean (Patel & Read, 1996). For example, if the height of a building is generally distributed with a mean of 100 feet and a standard deviation of 20 feet, you can predict that about 68% of buildings will be between 80 feet and 120 feet.
The Reason for Normal Distribution:
The height of a building is a continuous variable that is likely to be normally distributed. This is because several factors, such as the amount of land available, the zoning regulations, and the construction cost, determine the height of a building. These factors are all likely to be normally distributed, which means that the height of a building is also likely to be normally distributed.
Factors Leading to Variable Deviation:
Several factors could result in the variable of the height of a building deviating from the normal distribution, such as the changing of zoning regulations; this is precisely what happened in most of the cities downtown (Schläpfer, Lee & Bettencourt, 2015); also, the increasing cost of construction or the availability of land, these factors could cause the mean or standard deviation of the height of buildings to change, which would result in the variable deviating from the normal distribution.
Conclusion
The mean and the standard deviation characterize the normal distribution. The mean represents the center of the distribution, while the standard deviation represents the spread or variability of the data around the mean. It is important to note that the normal distribution is just a model (Livingston, 2004). In my example, the actual height of a building may not follow the normal distribution.
References
Livingston, E. H. (2004). The mean and standard deviation: what does it all mean? Journal of Surgical Research, 119(2), 117-123.
Schläpfer, M., Lee, J., & Bettencourt, L. (2015). Urban skylines: building heights and shapes as measures of city size. arXiv preprint arXiv:1512.00946.
Patel, J. K., & Read, C. B. (1996). Handbook of the normal distribution (Vol. 150). CRC Press.
Zucchi, Kristina. (2019). Lognormal and Normal Distribution. Retrieved from
https://www.investopedia.com/articles/investing/102014/lognormal-and-normal-distribution.asp