The paper aims to analyze using mathematical methods, a statistical model, considering as a case study an AUTO service in rural areas so that, under restrictive conditions generated by COVID-19 and compared to similar periods in previous years, it was possible to optimize the profit obtained by to the company manager. The study was conducted based on a mechanical workshop, "Vest Transcom", from which we evaluated the correlation coefficient. The mechanical workshop is located in the rural area of Caraș-Severin County. The analyzed period was one month during the pandemic, respectively May 2021. The correlation coefficient is the one that measures the degree of independence between two quantities. Some of the parts in the workshop were highlighted. Their cost and the total cost of a mechanical repair were evaluated. The authors continued the study by analyzing the dependence of labor price, this time as a function of the total price of parts (primary and secondary) it was observed that the second-degree polynomial model better approximates the phenomenon, R2 = 0.85. The mathematical function that describes the analyzed model is of several variables, so the factors generated favorable opinion for the business by the age of the car park in rural areas and the distance to large cities with CAR REPRESENTATIONS for different brands. From the statistical interpretation of the experimental data which represents a sample of the total parts contained in the ”Vest Transcom” workshop, we can conclude that the ratio between the costs of parts and the repair price induced by the exchange of a certain one is the best possible because the correlation coefficient has a positive value less than 1. Given the pandemic context, the mechanical workshop "Vest Transcom" worked very well, given that the car fleet from the rural area mostly includes old cars, which always need maintenance and upkeep, even if people have travelled less, there were still many cars to be repaired, so it is very necessary to have car workshops in the rural areas.

rural environment, mechanical workshop, mathematical analysis

environmental engineering

Presentation: None