2022 NJC P2 Q6
Every weekday morning, Jo arrives at the bus stop nearest to her home to catch bus $156$ to Bishan MRT station. The waiting time for bus $156$ follows a normal distribution with mean $9$ minutes and standard deviation $1.5$ minutes, and the time taken for the journey from the bus stop to Bishan MRT station follows a normal distribution with mean $10$ minutes and standard deviation $1.1$ minutes.
(i)
Find the probability that the mean waiting time for bus $156$ on $50$ randomly chosen weekdays exceeds $9.3$ minutes.
[3]
(ii)
Explain why your calculations in part (i) would still be valid even if the waiting time for bus $156$ on a weekday is not known to be normally distributed.
[2]
(iii)
If the train at Bishan MRT station leaves at 7.00 am, find the latest time (correct to the nearest minute) that Jo has to reach the bus stop if she misses the train less than $30\%$ of the time.
[2]
(iv)
In the following year, the waiting time for bus $156$ is increased by $30\%$ due to COVID-19 infections among bus drivers. Find the probability that the waiting time for a randomly chosen bus $156$ in the following year differs from the original waiting time for a randomly chosen bus $156$ by at most $2$ minutes.
[3]
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