QUESTION 1 Mark: 2+1+2 = 5 The checking-in time at a hotel is to be investigated. Historically, the process has had a standard deviation of 0.146. The means of 40 samples of 15 observations each given in minute in the table below: Sample 1 2 3 4 5 6 7 8 9 10 Mean 3.86 3.90 3.83 3.81 3.84 3.83 3.87 3.88 3.83 3.80 Sample 11 12 13 14 15 16 17 Mean 3.88 3.86 3.85 3.82 3.83 3.86 3.82 3.85 3.84 3.82 Sample 21 22 23 24 25 26 27 Mean 3.85 3.89 3.84 3.86 3.87 3.90 3.86 3.83 3.85 3.85 Sample 31 32 33 34 35 36 37 38 39 40 Mean 3.84 3.92 3.87 3.84 3.82 3.88 3.85 3.81 3.86 3.83 18 28 19 20 29 30 a i. iii. Construct a mean control chart for this process of checking-in with three-sigma (z = 3) limits. Is the process in control? Analyze the data using the median run-test and the up/down run-test and provide your conclusion