The manager of Motel 11 has 316 rooms in Palo Alto, California. From observation over a long period of time, she knows that on an average night, 268 rooms will be rented. The long-term standard deviation is 12 rooms. This distribution is approximately mound-shaped and symmetrical. (a) For 10 consecutive nights, the following numbers of rooms were rented each night.
Night 1 2 3 4 5
Number of rooms 234 258 265 271 283
Night 6 7 8 9 10
Number of rooms 267 290 286 263 240
Make a control chart for the number of rooms rented each night, and plot the preceding 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.)
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Looking at the control chart, would you say the number of rooms rented during this 10-night period has been unusually low? unusually high? about what was expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III).
The room rentals seem unusually high; out-of-control warning signal II is present. The room rentals are about what would be expected; no out-of-control warning signals are present. The room rentals seem unusually low; out-of-control warning signal III is present. The room rentals are about what would be expected; out-of-control warning signal I is present.
(b) For another 10 consecutive nights, the following numbers of rooms were rented each night.
Night 1 2 3 4 5
Number of rooms 238 245 261 269 273
Night 6 7 8 9 10
Number of rooms 250 241 230 215 217
Make a control chart for the number of rooms rented each night, and plot the preceding 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.)
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Would you say the room occupancy has been high? low? about what was expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III).
The room rentals are about what would be expected; no out-of-control warning signals are present. The room rentals seem unusually high; out-of-control warning signal III is present. The room rentals seem unusually low; out-of-control warning signals I and III are present. The room rentals seem unusually low; out-of-control warning signal I is present.