Align clock times before comparing normal travel times

The last weekday train leaves Bedok at 11.29pm. Its travel time $X$ to Redbridge is normal with mean 30 minutes and variance 9.

(i) Find the travel time exceeded by 90% of trips.2 marks

At 11.40pm Abel starts walking to Redbridge; his walking time $Y$ is normal with mean 16 minutes and variance 4.

(ii) Find the probability that the train arrives after midnight and Abel arrives before midnight.2 marks

(iii) Find the probability that Abel does not miss the train.4 marks

(iv) Explain why(iii) is greater than (ii).1 mark

Dina’s walking time $W$ has mean 4 minutes and variance 6.

(v) Explain why $W$ is unlikely to be normal.1 mark

(vi) For 40 random trips, find the probability that Dina’s sample mean is below 3.5 minutes.2 marks