The stated goal of a chain of service stores is to provide a lube and oil change for anyone's automobile in 15 minutes. The manager at one store thinks that there is a growing disparity among his workers in the time it takes to lube and change the oil of an automobile. To monitor this, the manager has selected a sample of 20 days and has recorded the time it took five randomly selected employees to service an automobile. The data are found below. Complete parts a through d. Click the icon to view the data. a. The manager noticed that the longest time it took to service a car was 25.21 minutes. Suppose the distribution of times to service a car was normal, with a mean of 15. Without analyzing the sample data, use your knowledge of a normal distribution to give the manager an estimate for the population standard deviation for the time it takes to service a car. The standard deviation is minutes. (Round to two decimal places as needed.) b. Use the data to construct an x- and an R-chart. Construct a control chart for the range. Which graph below shows an R-chart for the data? A. 16- 12- 8- 4- 0- 0 10 20 B. 167 12- 8- 4- MM 10 20 C. 167 12- 8- 4- 10 20 D. 16- 12- 8- 4- 10 MA 20 Construct a control chart for the mean. Which graph below shows an x-chart for the data? A. 20 Q B. 20 Q 10+ 0 10 20 10- 10 C. 20- www. D. Q Q 20- 10- 0 10 20 10- 0 10 20 c. Based on these data, what would you conclude about the service process? A. Since sixteen consecutive points are alternating up and down on the R-chart, the process is out of control. B. Since all of the points on the R-chart and X-chart are between the control limits, the process is under control. C. Since one point on the x-chart is below the lower control limit, the process is out of control. D. Since one point on the R-chart is above the upper control limit, the process is out of control. Employee Day 1 2 3 4 5 -234567 15.07 18.30 13.54 11.67 11.66 12.72 18.36 12.89 15.44 12.50 14.00 13.29 11.20 16.83 24.88 17.55 14.69 13.31 14.44 15.92 11.47 18.09 13.10 16.14 21.06 13.78 16.59 19.84 7.09 17.22 12.54 16.48 13.42 16.68 17.85 8 14.44 16.28 15.00 16.72 16.13 9 15.63 15.19 13.08 15.38 15.02 10 15.05 14.35 15.45 18.60 14.07 11 15.12 13.04 13.88 16.58 12.46 12 25.21 14.13 14.39 15.56 13.32 13 13.76 15.48 19.17 20.31 16.62 14 16.65 12.65 15.18 12.59 16.16 15 14.90 12.57 16.29 13.96 16.54 16 13.84 12.04 15.70 18.26 11.35 17 17.26 16.45 11.35 13.21 15.06 18 16.36 13.16 14.16 16.96 12.45 19 12.21 15.08 16.14 15.15 12.40 20 12.79 17.16 15.12 16.65 13.03