The times taken by buses to travel between two stops on a route follow a normal
ID: 3133186 • Letter: T
Question
The times taken by buses to travel between two stops on a route follow a normal pattern of variation with a mean of 13.9 minutes. A commuter makes this journey ten times each week. One week she times the ten journeys and works out that the standard deviation of them is 1.7 minutes. Treating the ten journeys in a week as a random sample:
(a) what mean journey time will be exceeded one week in twenty?
(b) what mean journey time will be exceeded one week in forty?
(c) what mean journey time will not be exceeded 90% of the time?
Explanation / Answer
a)
1 week in 20 = 5% of the time, so two standard deviations or 1.65*1.7 + 13.9 = 16.71 minutes. Use NORMSINV(0.95) in excel
c) 1 week in 40 = 2.5% of the time or (97.5 percentile) = 1.96 standard deviations 1.96*1.7 + 13.9 = 17.23 minutes. Use NORMSINV(0.975) in excel.
c)90% = 1.28 standard deviations from the mean, so 1.28*(1.7) + 13.9 = 16.08 Minutes. Use NORMSINV(0.9) in excel.
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