Could you please answer and show calculations

20. A teller at a drive-up window at a bank had the following service times (in minutes) for 20 randomly selected customers. SAMPLE 1 2 4 4.5 4.6 4.5 4.7 4.2 4.5 4.6 4.6 4.2 4.4 4.4 4.8 4.3 4.7 4.4 4.5 4.3 4.3 4.6 49 a. Determine the mean of each sample. b. If the proceu parameters are unknown, estimate its mean and standard deviation c. Estimate the mean and standard deviation of the sampling distribution d. What would three-sigma control limits for the process be? What alpha risk would they provide? e. What alpha risk would control limits of 4.14 and 4 86 provide ? f. Using limits of 4.14 and 4.86, are any sample mean beyond the control limits? If so, which one(t)? Construct control charts for means and ranges using Table 10.3. At any samples beyond the control limits? If so, which one()? h. Explain why the control limits are different for means in parts d and . 1. If the process has a known mean of 4.4 and a known standard deviation of 18, what would three-sigma control limits be for a mean chart? Are any sample means beyond the control limits? If so, which one(s)? 21. A process that products com shine... 1 - 12.11, R = .046 and Az -.73 for n=4 (from Table 10.3 ). Using Formula 10-2, we can compute the upper and lower limits for a mean control chart TABLE 103 Factors for three-sigma control limits for X and R charts FACTORS FOR R CHARTS Number of Observations in Factor for Lower Control Upper Control Sample, Chart, Limit R Az Dy DA 1.88 0 3.27 3 1.02 0 2.57 0.73 0 2.28 5 0.58 0 2.11 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.13 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.63 16 0.21 0.36 1.84 17 0.20 0.36 1.62 16 0.19 0.39 1.61 19 0.19 0.50 1.80 20 0.18 0.41 1.59 UCL = 12.11 + 730016) = 12.14 mics LCL = 12.11 - 73015) = 12.08 ininus