Question

Consider this scenario:
You are in charge of a manufacturing facility that produces an automotive part (steel shaft for the gearbox) with an acceptable dimension of 2.5±0.05 inches in diameter. Note that, the most desirable product is one with diameter of exactly 2.5 inches. Two vendors are trying to sell you their machines for the shaft-machining task. You have to select a vendor.

You asked both vendors to supply data on the machining accuracy of their machines 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
Vendor A: X has a normal distribution with mean 2.48 and variance 0.001
Vendor B: X has a normal distribution with mean 2.51 and variance 0.002

Answer the following:

Examine the scenario as described and discuss what additional information would be helpful to make this decision and why that information would be useful. (50 words)

Assuming that you have to select a vendor using only 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. (200 words or less)

Answer 1