A company, Steelten, produces frictionless linear sleeves to slide over guide rods. Listed below are 50 sample measurements from the inside dimensions of the sleeve. These samples were taken by selecting a sleeve at random each 15 minutes from the production process. Drawings state that the inside dimensions of the sleeve must be greater than 5.000007 mm with a + .005 mm tolerance. Management wants to determine whether this process is capable of meeting the stipulated specification.

a. Construct a histogram of these data and comment on their normality.
b. Construct a histogram of these data and comment on their normality.
c. Use Minitab to construct X and MR charts using a Box-Cox transformation with optimal λ to generate a transformed pair of control charts. Comment on the state of statistical control for the transformed data. What value of λ was used in the transformation?

e. Use the raw data in part a and then the results derived from the two pairs of charts (constructed in parts b, c, and d respectively) to estimate the percentage of output that you estimate will exceed the single specification limit. Compare the results of the four approaches. Which one would you recommend and why?

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Sample Observation Sample Observation 5.011476667 5.018806934 5.001875063 5.030795054 5.001027603 31 5.000444375 5.002040977 5.000172802 34 5.008660108 5.002222287 5.015723974 5.000905723 5.001694923 5.005671712 5.007475376 5.023444816 5.000006991 5.010427947 5.026445903 26 27 28 29 30 4 6 32 5.0176618133 5.000966222 5.004208677 5.011208867 5.002558834 35 36 37 5.00251526738 39 40 41 42 43 10 13 5.00349789 5.004492611 5.007460553 5.00503618 5.009858766 5.00078874 15 16 17 18 19 20 21 5.000148058 5.006262018 5.01177234 5.010279185 5.012454576 5.004531009 445.010487071 5.011158451 5.015782673 5.022627968 5.002943183 5.059122706 5.00459357 45 46 5.00020821447 48 49 50 5.001814537 5.00173855 5.004980822 5.008198258 5.012005428 24 25 and R