A Car Mechanic Is Thinking of Guaranteeing Customers That an Oil

question 8

Essay

A car mechanic is thinking of guaranteeing customers that an oil change will take no more than 15 minutes with a 99.73% confidence level. He takes a few samples of size 5 and finds the process mean to be 13 minutes with a standard deviation of .2 minutes and average sample range of 1.2 minutes. Find the A₂, D₄, and D₃ values and use them to compute the upper and lower limits for an x-bar chart. Use the upper limit to determine if the mechanic can offer a 15 minute guarantee. Assume the mechanic plots the samples on the x-bar control chart and finds the process is in control, is there anything else the mechanic is missing to ensure the process is in control?

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Definitions:

Marx

Karl Marx, a 19th-century philosopher, economist, and revolutionary, known for his theories about capitalism and communism.

Weber

Refers to Max Weber, a German sociologist, economist, and political scientist known for his theory on the process of rationalization and his analysis of bureaucracy and social stratification.

Social Stratification

The division of society into hierarchical levels based on factors like wealth, power, and status, leading to unequal access to resources and opportunities.

Inequality

The unequal distribution of resources, opportunities, rights, and powers within a society.