hwk1_sol - ISOM 111 L6-L7, Fall 2009 1 Homework 1 Solutions...

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ISOM 111 L6-L7, Fall 2009 1 Homework 1 Solutions I . Problem 2.18 and 2.38 + additional part (g): The Bank Customer Waiting Time Case: Table 1.6 (page 11) presents the waiting times for teller service during peak business hours of 100 randomly selected bank customers. Fig- ures 2.27-2.29(b) give the MINITAB and the MegaStat outputs of statistics describing the 100 waiting times. (a) Does the sample mean 5.46 provide evidence that the mean of the population of all possible customer waiting times during peak business hours is less than six minutes (as is desired by the bank manager)? Explain your answer. Ans : The sample mean of 5.46 does provide evidence that the mean of the population of all possible customer waiting times during peak business hours is less than six minutes. The reason is that when the sample size is big (100 in this example), the sample mean is (with high probability) close to the population mean. (b) Use the stem-and-leaf display in Figure 2.17 (page 52) to verify that the median of the waiting times is 5.25. How do the mean and median compare? What does the stem-and-leaf display tell you about why they compare this way? Ans : The sample size is 100, hence the median is the average of the 50th and 51st values when the data are arranged in increasing order. From the stem-and-leaf display one finds that these two values are 5.2 and 5.3, hence the median is (5 . 2 + 5 . 3) / 2 = 5 . 25. The mean 5.46 is slightly larger than the median. This is due to the fact that the distribution is slightly skewed to the right (see the stem-and-leaf display in Figures 2.17 and also the histogram in Figure 2.18). (c) The mean and the standard deviation of the sample of 100 bank customer waiting times and 5.46 and 2.475 respectively. What do the stem-and-leaf display and histogram in Figures 2.17 and 2.18 (pages 52) say about whether the Empirical Rule should be used to describe the bank customer waiting times? Ans : The histogram is bell-shaped (even though slight skewed to the right). Hence it is reasonable to apply the Empirical Rule. (d) Use the Empirical Rule to calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all possible bank customer waiting times. (Read the first paragraph on p.68 for the definition of tolerance intervals.)
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ISOM 111 L6-L7, Fall 2009 2 Ans : By the Empirical Rule, the three tolerance intervals are given by [¯ x ± s ], [¯ x ± 2 s ] and x ± 3 s ] respectively. Plugging ¯ x = 5
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This note was uploaded on 01/01/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Spring '09 term at HKUST.

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hwk1_sol - ISOM 111 L6-L7, Fall 2009 1 Homework 1 Solutions...

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