A person wants to know whether Route A or Route B is the better commute to work. He also wants to know which route is the better commute home. He times the commutes (in minutes) to work by both routes many times (see Fig. 74) and also times the return trip home by both routes many times (see Fig. 75). In each direction (toward work and toward home), the mean commute time by Route A is 25 minutes and the mean commute time by Route B is 29 minutes. In one direction, the standard deviations for Routes A and B are both 5 minutes. In the other direction, the standard deviations for Routes A and B are both 1 minute.
Fig. 74

Fig. 75

a. In which direction, toward work or toward home, were the standard deviations for Routes A and B both 5 minutes? Explain.
b. In which direction, toward work or toward home, were the standard deviations for Routes A and B both 1 minute? Explain.
c. Refer to the given means and standard deviations to explain why the distribution for commuting to work is bimodal but the distribution for commuting to home is unimodal.
d. When determining how different the commute times for Route A are from the commute times for Route B, explain why it is not enough to simply compare the mean times.

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Commute to Work 20 15 10 E 24 26 28 30 32 Minutes Commute to Home 20 15 10 10 15 20 25 30 35 40 45 Minutes