A calculator is assembled from 171 components, each one made by a process capable of a 2 standard deviation level (95.5% reliable).
a) What is the reliability of the calculator? (Enter your response as a percentage rounded to eight decimal places)
b) If you want the calculator to be at least 99.95% reliable, what should the reliability of each component be? Assume that all the components will have the same reliability. (Enter your response as a percentage rounded to eight decimal places).
c) If each component is made by a 6 standard deviation capable process (99.9999998% reliable), how reliable will the calculator be? (Enter your response as a percentage rounded to eight decimal places).
Please show work step-by-step.