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Tail probabilities

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Curiously, this value is the tail area beyond 4.5 standard deviations from the mean; i.e., Pr (Z > 4.5) = Pr (Y > + 4.5 ) = 0.000 003 398. The 4.5 standard deviations is the difference between 6 (the idea from which the program takes its name) and an assumed 1.5 shift of the process centre from the mean. The vertical axis in each of the six diagrams shown overleaf is labelled f (z); give both the name and the equation for f (z). ? Explain briefly. Answer the same question if the Signs were replaced by < signs. How would the values of the tail probabilities given above be affected if the > signs in the inequalities were replaced by ? Explain briefly. Why are the absolute value signs used in the two-tail probability expressions above?


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