15. A technician in a quick oil change shop had the following service times (in minutes) for 20 randomly selected cars: @ Sample 1 2 3 4 4.5 4.6 45 47 4.2 45 4.6 46 42 44 4.4 48 43 47 4.4 45 43 4.3 4.6 49 a. Determine the mean of each sample. b. Estimate the mean and standard deviation of the process. c. Estimate the mean and standard deviation of the sampling distribution of the sample mean. d. What would three-sigma control limits for the sample mean be? What alpha risk would they provide? e. What alpha risk would control limits of 4.14 and 4.86 for the sample mean provide? f. Using the control limits of 4.14 and 4.86, are any sample means beyond these control limits? If so, which one(s)? g. Construct the control charts for sample mean and sample range using & Table 10-3. Are any sample means and ranges beyond the control limits? If so, which one(s)? h. Explain why the control limits are different for sample mean in parts d and g. . If the process has a known mean of 4.4 and a known standard deviation of 0.18, what would three-sigma control limits be for a sample mean chart? Are any sample means beyond the control limits? If so, which one(s)