ISOM 111 L6L7, 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 2.272.29(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 stemandleaf 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 stemandleaf
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 stemandleaf 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 stemandleaf 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 stemandleaf 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 bellshaped (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 L6L7, Fall 2009
2
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 Spring '09
 AnthonyChan
 Standard Deviation, Bond Funds, ISOM, stemandleaf display, asset allocation mix

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