In the City of Pickering fire department, the number of labor-hours lost each day because of accidents and work related injuries is a normally distributed random variable with a mean = 30 and a standard deviation of 8. At the end of each day, the number of lost hours is recorded. At week's end the five daily observations are treated as a subgroup, and the average and range are plotted on control charts.

a. For the X-bar chart, what values should be used for the center line and the 1-sigma, 2-sigma, and 3- sigma limits? What assumptions must you make to use the data given previously in setting up an X-bar chart? b. Answer part a for the R chart. c. What limits would be appropriate if they want to plot each day's lost hours rather than weekly averages? Would these control limits be accurate in this case? Explain in detail. d. If daily labour lost were not normally distributed, what limits should be used for the weekly - X chart? Could they use a daily chart? Explain in detail.