Question

A national restaurant chain is composed of 6500 restaurants, each of which is located in close proximity to an interstate highway. The restaurant's business strategy is to serve its core customer base: people travelling on the interstate highway system who are looking for a quality dining experience. Customers generally enjoy the restaurant chain's menu, atmosphere, and consistency from restaurant to restaurant. The company's leadership, located at corporate headquarters, is very interested in the relationship between the cost of a gallon of gasoline and the company's revenue. Specifically, the company is concerned that if gasoline prices rise in the near future, the company's revenue will decline dramatically. The company's research department recently collected data for analysis in order to support leadership's upcoming discussion of whether the company should expand and diversify to locations away from an interstate highway. Annual revenue figures from a random sample of 150 restaurants were collected. The research division also collected and calculated the average annual cost of gasoline at these 150 restaurants by randomly selecting three gasoline stations near each restaurant. Historical data was then used to calculate the average annual cost of gasoline. The Restaurant Number, Geographic Region, Annual Revenue, Average Cost of Gasoline, Miles from the Interstate, Square Footage and Annual Increase in Revenue were collected for these 150 restaurants. Create a histogram with a 0.20 bin width of the Average Cost of Gasoline data. From your visual analysis, describe the shape and center of the distribution. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to the nearest tenth as needed.)

A. The distribution is right-skewed with the typical Average Cost of Gasoline around $ (fill in the blank) enter your response here.
B. The distribution is left-skewed with the typical Average Cost of Gasoline around $ enter your response here. (fill in the blank)
C. The distribution is symetric and unimodal with the typical Average Cost of Gasoline around $ (fill in the blank) enter your response here.
D. The distribution is bimodal with the typical Average Cost of Gasoline around $ (fill in the blank) enter your response here. thank you!

Answer 1

Unable to provide a histogram or descriptive analysis of the distribution without actual data. Generally, higher gasoline prices can lead to reduced consumer use, potentially affecting businesses reliant on travel, such as a restaurant chain along interstates. Gasoline price fluctuations are critical for the company's revenue analysis.

Step-by-step explanation:

To create a histogram and describe the shape and center of the distribution for the Average Cost of Gasoline data, you would first use the collected information to construct a histogram with a bin width of 0.20. However, without the actual data, it's not possible to construct a histogram or describe its shape and center.

Nevertheless, we can discuss general trends based on economic principles. When the price of gasoline increases above the equilibrium price, as illustrated by a price change from $1.40 to $1.80 per gallon, the quantity demanded of gasoline drops. This reflects consumer behavior in reaction to higher gasoline prices, where they tend to use less gasoline. Similarly, when prices are below equilibrium, say at $1.20 per gallon, the quantity demanded would increase, as consumers would be more inclined to use gasoline more freely, reflected in actions like taking longer trips or warming up the car longer in the winter. But the incentive for gasoline producers to produce and sell gasoline would decrease, potentially affecting supply.

For the restaurant chain in question, if the analyzed data shows a large variability or significant spikes in gasoline prices, the company might be concerned about potential declines in customer visits, as higher gas prices could deter travel and, in turn, dining at the restaurants located along the interstate highways.

Answer 2

A histogram with a 0.20 bin width cannot be created without the actual data. The shape and center of the distribution are unknown without visualizing a histogram from the dataset. Hypothetical examples illustrate how gas prices above or below equilibrium can affect demand.

Step-by-step explanation:

To create a histogram with a 0.20 bin width of the Average Cost of Gasoline data, we would organize the data into intervals of $0.20 and count the number of entries that fall into each bin. The center of a distribution refers to the point where the data clusters, often observed as the peak of a histogram. The shape can be symmetric, where the data tails off equally on both sides of the center, right-skewed (long tail on the right side), left-skewed (long tail on the left side), or bimodal (two clear peaks). Without the actual dataset to visualize a histogram, we cannot accurately describe the shape and center of the distribution.

Regarding the hypothetical situation provided, the average cost of gasoline for the 16 gas stations would follow a normal distribution assuming the central limit theorem applies, due to the sample size being greater than 30. However, since the given actual sample size is 16, which is less than 30, and the population distribution of gas prices is unknown, caution must be taken in assuming normality.

In economics, if the price of a gallon of gasoline is set above the equilibrium price, quantity demanded will decrease, reflecting a consumer reaction to the higher price. Conversely, if the price is below the equilibrium, the quantity demanded will increase, as consumers take advantage of the lower price.