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Part $1$

A popular U$.$S$.$ automobile manufacturer has$10,000$ dealerships located throughout the country. The automobile manufacturer has multiple brands within its$$ portfolio: a value brand that caters to younger$$ clientele, a moderate brand that caters to middle class customers and$$ finally, a premium brand which is marketed to wealthy clientele. The$$ company's leadership, located at corporate$$ headquarters, is very interested in the relationship between the median salary of potential customers and the$$ company's revenue.$$ Specifically, the company is concerned that if potential$$ customers' salaries continue to not increase in the$$ future, the$$ company's revenue will remain$$ stagnant, which will in turn steer away potential investors and shareholders. The$$ company's research department recently collected data for analysis in order to support$$ leadership's upcoming discussion with shareholders and investors about the$$ company's future revenue forecast. Sales figures from a random sample of $1000$ dealerships were collected. The research division also conducted statistical$$ analysis, using data provided by the Bureau of Labor and$$ Statistics, to calculate the median salary of people living in the vicinity of these$1,000$ dealerships. The Dealership$$ Number, State, Median$$ Salary, Annual$$ Sales, Number of Vehicles$$ Sold, Square Footage and Quality Award Winner data were collected for these $1000$ dealerships.

what is the $95\%$ lower limit$?$