Question

Yellowstone Park Medical Services (YPMS) provides emergency health care for park visitors. Such health care includes treatment for everything from indigestion and sunburn to more serious injuries. A recent issue of Yellowstone Today (National Park Service Publication) indicated that the average number of visitors treated each day by YPMS was 21.7. The estimated standard deviation was 4.2 (summer data). The distribution of numbers treated is approximately mound-shaped and symmetric.

(a) For a 10-day summer period, the following data show the number of visitors treated each day by YPMS.

Day	1	2	3	4	5	6	7	8	9	10
Number treated	25	19	17	15	20	24	30	19	16	23

Make a control chart for the daily number of visitors treated by YPMS, and plot the data on the control chart. (Be sure to include the horizontal lines on the control chart. Recall that the mean line is solid and the control limit lines are dashed.)

Do the data indicate that the number of visitors treated by YPMS is "in control"? Explain your answer.

The data indicate the process is in control; no out-of-control warning signals are present.The data indicate the process is out-of-control; out-of-control warning signal I is present.    The data indicate the process is out-of-control; out-of-control warning signal III is present.The data indicate the process is out-of-control; out-of-control warning signals I and III are present.

(b) For another 10-day summer period, the following data were obtained.

Day	1	2	3	4	5	6	7	8	9	10
Number treated	20	15	12	21	24	28	32	36	35	37

Make a control chart, and plot the data on the chart. (Be sure to include the horizontal lines on the control chart. Recall that the mean line is solid and the control limit lines are dashed.)

Do the data indicate that the number of visitors treated by YPMS is "in control" or "out of control"? Explain our answer. Identify all out-of-control signals by type (I, II, or III).

The data indicate the process is out-of-control; out-of-control warning signal I is present.The data indicate the process is out-of-control; out-of-control warning signal III is present.    The data indicate the process is out-of-control; out-of-control warning signals I and III are present.The data indicate the process is in control; no out-of-control warning signals are present.

If you were the park superintendent, do you think YPMS might need some (temporary) extra help?
---Select--- Yes No

Answer 1

a) A control chart for a variable x is a plot of the observed values (vertical scale) and the number of visitors treated. Place horizontal lines at The mean is: μ-21.7 and the standard deviation is σ-4.2 Control limits-Įt3ơ - 21.7+3(4.2 21.7+12.6 -9.1,34.3 Control limits-μ 2σ 21.7+2(4.2) 21.7+8.4 -13.3 and 30.1

寸 2 μ+3σ 6"き μ-2σ μ-3σ 2 8 10 6

The x are more or less evenly distributed about the mean u 21.7. None of the points are outside the ut3o limit, it appears that x distribution is in under control b) A control chart for a variable x is a plot of the observed values (vertical scale) and the number of visitor treated Control limits-μ 2σ -26.5+2(8.73) 26.5+17.46 9.04,43.96

Control limits- I 26.5 +3(8.73) -21.7+26.19 0.31 and 52.69 μ-3 σ 10 YPMs is out of It is observed that the data indicate the number of visitors treated by control. That is process is said to be out of control.