A dental clinic is studying how long patients wait to see the dentist or dental hygienist. For every patient, waiting times are measured as the number of seconds from registration to first contact with the dentist or dental hygienist. At the end of each day, the times are entered in a row of a spreadsheet. The number of patients varies from day to day. To keep the analysis simple, an option in the spreadsheet software to randomly pick a fixed number of observations can be invoked; in particular, n = 5 was chosen. Defining a given day as a sample (or subgroup), below are data for 20 consecutive days: Day x1 x2 x3 x4 x5 xbar R 1 839 585 583 613 768 ? ? 2 706 527 956 644 612 689.0 429 3 322 614 807 282 170 439.0 637 4 1001 904 419 522 430 655.2 582 5 259 811 847 603 572 618.4 588 6 681 523 665 397 873 627.8 476 7 799 874 553 173 296 539.0 701 8 263 585 546 445 455 458.8 322 9 591 637 739 927 825 743.8 336 10 372 997 496 283 641 557.8 714 11 633 371 425 625 752 561.2 381 12 294 522 599 740 468 524.6 446 13 714 600 738 694 610 671.2 138 14 311 829 216 447 506 461.8 613 15 720 446 393 431 707 539.4 327 16 306 550 633 845 394 545.6 539 17 561 574 370 495 580 516.0 210 18 431 500 580 349 626 497.2 277 19 404 791 773 576 1073 723.4 669 20 640 687 754 627 482 638.0 272 a. Compute the sample mean and sample range (shown as a question mark in the table) for day 1. b. Compute the grand mean and the average range . c. Calculate the and control chart limits for these data. Is the process in statistical control? NOTE: You do not need to plot the control charts, just check whether the statistics plotted on these charts fall within the control limits and then conclude whether the process is in control or not. d. Estimate the (unknown) true mean and standard deviation of the process generating the individual (waiting time) measurements. e. Experience suggests that people generally become dissatisfied when having to wait more than 15 minutes. Based on your estimates in part b, estimate the probability that a patient will have to wait 15 minutes or more (i.e. estimate the fraction (or proportion) of patients that will wait 15 minutes or more). Assume that the waiting time variable can be well approximated by the normal distribution. (Hint: use the normal curve areas to compute this quantity) f. Suppose that USL = 15 minutes and LSL = 0 minutes, what conclusions would you draw about process capability of this dental clinic? That is, calculate/estimate the potential capability of the process and the actual process capabilities. , . Comment on the results.