Sarah Paterson Quiz 1_quiz1.xlsx - 1 A popular approach to management which originated at Motorola is called Six Sigma While there are currently many

Sarah Paterson Quiz 1_quiz1.xlsx - 1 A popular approach to...

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1. A popular approach to management, which originated at Motorola, is called Six Sigma. While there are currently many components of Six Sigma, it was originally conceived as a way to talk about the capability of a process to meet customer specifications or requirements. Motorola desired that all of their processes could be so good that the distance between the target and any specification would be six standard deviations. They said that, assuming that the process output was normally distributed, only 3.4 defects would be produced for every million parts produced, even when the mean shifted by 1.5 standard deviations. Consider a process that produces metal rods that will be used as a component to construct aircraft. An important characteristic of the rods is their tensile strength, measured in pounds per square inch (psi). Historically, parts have been normally distributed with a mean strength of 10,500 psi with a standard deviation of 300 psi. The customer requires that the strength of the rod be at least 9,400 psi. a. What is the probability that a single part will have a strength that is below 9,400 if the mean shifted down from its historical value by 1.5 standard deviations? Indicate your answer in cell B3 of the Answer Summary sheet. Show your work on this sheet, on the Strength Data sheet or on a new sheet. (Your "work" may just be one formula.) b. What would the specification have to be (rather than 9,400) so that the probability of producing a defective (weaker) part was 3.4 parts per million (i.e., .0000034)?
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