Normal Distribution in Scheduled Bus Arrivals
Normal Distribution in Scheduled Bus Arrivals
John goes to school by bus. His arrival time at the bus interchange is normally distributed with mean 7.00 am and standard deviation 2 minutes. Buses are scheduled to leave promptly every 5 minutes from 6.31 am.
- If John always gets on the first bus that arrives, find the probability that he catches the bus at
- 6.56 am
- 7.01 am
- 7.06 am
- John will be late for school if he catches a bus after 7.06 am. Assuming that the standard deviation of the arrival time remains the same, determine the new mean arrival time that will ensure that, on average, he is not late for school for more than one day in a five-day week.
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Answer:(a)(i) \(0.0227\) (ii) \(0.669\) (iii) \(0.307\) (b) Latest mean approximately \(7.04{:}19\text{ am}\); if scheduling only whole minutes, no later than \(7.04\text{ am}\)
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