Mr. Taccagno is the President of a company that makes automobile components. Unfortunately, he received complaints recently about the quality of one specific part. Mr. Taccagno asks his Chief Engineer, Mr. Pensamolto, what should be done. Mr. Pensamolto tells him that all quality problems result from one machine and that for only $150K, he can buy a new machine that will solve the problem. Mr. Taccagno is skeptical about spending this money, so he hires you as a consultant to determine the quality of the existing machine. The most common product this machine makes has a specification of 8.50 0.51. You run 250 samples of product on the current machine, finding a normal distribution with a mean of 8.41 and a variance of 0.027. Mr. Taccagno does not care about opinions. He wants solid evidence regarding this purchase decision. Based on the results of your experiment, do you agree with Mr. Taccagno (don't buy the machine) or Mr. Pensamolto (buy the machine)? Show your reasoning using quantitative methods. (You must show work for credit. Like Mr. Taccagno, I also have little interest in unsupported claims.)