statistics writting

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