# probability and statistics homework

Problem description: You oversee a manufacturing facility that produces an automotive part (steel shaft for the gearbox). The acceptable dimension of the shaft is 2.5±0.05 inches in diameter with the most desirable product being exactly 2.5 inches. Two vendors are trying to sell their equipment for the shaft-machining task to your company, Automotive Parts Corporation. You have been asked to assess the equipment from each vendor, and to make a recommendation on which one to make the purchase from, supported by a justification for your decision.

You asked both vendors to supply data on the machining accuracy of their equipment for the given task. Both vendors machined 100 shafts, collected data, plotted histograms, fitted the histograms with normal distributions and supplied you with their findings

Let X= diameter in inches of the gearbox shaft
Ace Machines: X has a normal distribution with mean 2.48 and variance 0.001
Best Machinery: X has a normal distribution with mean 2.51 and variance 0.002

When you are completing your memorandum be sure to address the following:

• Recommend a vendor using the given information, develop and discuss your approach (give all details including quantitative justification). Your response to this question must be directed to the audience described below.
• Examine the scenario as described and discuss what additional information would be helpful to make this recommendation a stronger selection, and why that information would be useful. Be careful not to negate your recommendation as you explain this.
• Include your calculations as a titled addendum on its own page at the end of your document.

Audience: You are creating this document for the company’s Chief Operating Officer, Lin Gerard, and copying the Chief Financial Officer, Aileen Kitts. Documents involved in major financial decisions like this may also be distributed by the addressees to other executives and the corporate board members.

Document: Complete this assignment as a memorandum. Follow the guidance for provided in your reading. Utilize clear, professional language, including setting your Word preferences to check for a more professional writing approach. Examples of professional language constraints would include: