The Acme Widget Co. has been receiving complaints about the length of the widgets they are producing. The widgets are supposed to be 220.0 mm in length with a tolerance of plus or minus 0.5%. The project engineer measured 8 randomly selected widgets and found the following lengths (see table from picture). How many of the widgets in the sample do not fall within the manufacturer's specifications? (Show the range of acceptable lengths specified by the manufacturer). Calculate the mean and the variance of the widgets lengths. Determine the number of widgets (and list their values) that vary by more than one standard deviation from the mean.