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Understandable Statistics, Concepts and Methods

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 symmetric.

(a) For 10 consecutive nights, the following numbers of rooms were rented each night:

$$\begin{array}{l|cccccc}

\hline \text { Night } & 1 & 2 & 3 & 4 & 5 & 6 \\

\hline \text { Number of rooms } & 234 & 258 & 265 & 271 & 283 & 267 \\

\hline & & & & & & \\

\hline \text { Night } & 7 & 8 & 9 & 10 & & \\

\hline \text { Number of rooms } & 290 & 286 & 263 & 240 & & \\

\hline

\end{array}$$

Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Interpretation 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 you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III).

Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Interpretation 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 you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III).

(b) For another 10 consecutive nights, the following numbers of rooms were rented each night:

$$\begin{array}{l|cccccc}

\hline \text { Night } & 1 & 2 & 3 & 4 & 5 & 6 \\

\hline \text { Number of rooms } & 238 & 245 & 261 & 269 & 273 & 250 \\

\hline & & & & & & \\

\hline \text { Night } & 7 & 8 & 9 & 10 & & \\

\hline \text { Number of rooms } & 241 & 230 & 215 & 217 & & \\

\hline

\end{array}$$

Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Would you say the room occupancy has been high? low? about what you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or IIII).