Question

The normal distribution describes many common phenomena. Imagine a frequency distribution describing popcorn popping on a stovetop. Some kernels start to pop early, maybe one or two pops per second; after ten or fifteen seconds, the kernels are exploding frenetically. Then gradually the number of kernels popping per second fades away at roughly the same rate at which the popping began.

The heights of American men are distributed more or less normally, meaning that they are roughly symmetrical around the mean of 5 feet 10 inches. Each SAT test is specifically designed to produce a normal distribution of scores with a mean 500 and a standard deviation of 100. According to the Wall Street Journal, Americans even tend to park in a normal distribution at shopping malls; most cars park directly opposite the mall entrance—the “peak” of the normal curve—with "tails” of cars going off to the right and left of the entrance.

The beauty of the normal distribution—its Michael Jordan power, finesse, and elegance—comes from the fact that we know by definition exactly what proportion of the observations in a normal distribution lie within one standard deviation of the mean (68.2 percent), within two standard deviations of the mean (95.4 percent), within three standard deviations (99.7 percent), and so on. This may sound like trivia. In fact, it is the foundation on which much of statistics is built.

Find a study/article (related to business) in the news that uses the normal distribution to explain a phenomenon. Summarize the study and discuss how the study uses/apply the normal distribution. Makes sure to provide the link to the study/article.

Answer 1

Answer:

Let us consider the article in the news “Stochastic modelling of photovoltaic power generation and electricity prices”.

The study proposed a stochastic model for the maximal production of photovoltaic (PV) power on a daily basis, based on data from three transmission system operators in Germany. The study apply sun intensity as a seasonal function and model the deseasonalized data using an autoregressive process with skewed normally distributed noise, with seasonal variance to explain the stochastic dynamics. It is further demonstrated that the power spot prices are negatively dependent on the PV production. As an application of the results obtained by conducting the study there is a scope of discussion about the virtual power plant derivatives and energy quanto options, as well as continuous-time stochastic processes for PV and power spot price dynamics.

Link:

http.www.timesnews.com/ Stochasticmodellingofphotovoltaicpowergeneration/