Consider the 63 automatic teller machine (ATM) transaction times given in Table 3.6 above.
a. Construct a histogram (or a stem-and-leaf display) for the 63 ATM transaction times. Describe the shape of the distribution of transaction times.
b. When we compute the sample mean and sample standard deviation for the transaction times, we find that* = 36.56 and s = 4.475. Compute each of the intervals [ ± s], [ ± 2s], and [ ± 3s]. Then count the number of transaction times that actually fall into each interval and find the percentage of transaction times that actually fall into each interval.
c. How do the percentages of transaction times that fall into the intervals [ ± s], [ ± 2s], and [ ± 3s] compare to those given by the Empirical Rule? How do the percentages of transaction times that fall into the intervals [ ± 2s] and [± 3s] compare to those given by Chebyshev's Theorem?
d. Explain why the Empirical Rule does not describe the transaction times extremely well.