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 p and the actual process capabilities. pu, pt pk. Comment on the results

Day x2 lo 811 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: X1 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 5 259 847 603 572 618.4 588 6 681 523 665 397 873 627.8 476 7 799 874 553 173 296 539.0 701 263 585 546 445 455 458.8 322 9 591 637 739 927 825 743.8 336 372 10 997 496 283 641 557.8 714 633 11 371 425 625 752 561.2 381 12 522 599 294 740 524.6 468 446 13 714 738 600 138 694 610 671.2 14 829 311 216 447 461.8 506 613 707 327 15 446 393 431 539.4 720 16 845 545.6 539 550 306 394 210 495 561 574 580 370 516.0 17 349 500 626 580 497.2 18 277 431 723.4 669 19 404 1073 576 773 791 627 482 754 687 638.0 272 20 640 633