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The Boston Marathon. The Boston Marathon has been run each year since 1897. Winning times were highly variable in the early years, but control improved as the best runners became more professional. A clear downward trend continued until the 1980s. Rick plans to make a control chart for the winning times from 1950 to the present. The first few times are 153, 148, 152, 139, 141, and 138 minutes. Calculation from the winning times from 1950 to 2011 gives

134.032 minutes and s = 6.462 minutes

Rick draws a center line at and control limits at 3s for a plot of individual winning times. Explain carefully why these control limits are too wide to effectively signal unusually fast or slow times.

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