Final Answer:
The normal curve is prevalent in nature because many natural phenomena tend to cluster around an average value with symmetrical variations, following the central limit theorem. It's not solely a man-made construct or a perfect mathematical model but arises from the combined impact of multiple independent factors, resulting in a bell-shaped distribution. Thus the correct option is c).
Step-by-step explanation:
The normal curve's prevalence in nature stems from the tendency of numerous natural phenomena to exhibit behaviors that align with a bell-shaped distribution. This distribution often emerges due to the central limit theorem, where the combined effect of multiple random factors results in a symmetrical pattern around a mean value. In many biological, physical, and social systems, various factors contribute to observed outcomes, and when these factors act independently and additively, their collective effect tends to form a symmetrical pattern resembling the normal curve.
For instance, when measuring physical attributes like human height or weight, numerous genetic and environmental factors influence these traits. The central limit theorem predicts that as more independent factors contribute to the overall measurement, the distribution of heights or weights among a population will approximate a bell curve. This phenomenon isn't a purely man-made construct nor a perfect mathematical model; rather, it arises from the natural aggregation of multiple influences, leading to a pattern of central tendency and symmetric variations.
Mathematically, this can be demonstrated through various real-world examples where data clusters around a mean and exhibits symmetrical variations. Observations from diverse fields such as biology, economics, and physics consistently show this pattern, reinforcing the concept that many natural phenomena tend to align with the characteristics of the normal curve due to the cumulative impact of multiple contributing factors. Thus, the normal curve's ubiquity in nature arises from the convergence of numerous influences, resulting in a symmetrical distribution around a central value. Thus the correct option is c).