In order to go to university a student needs to catch a train at 8:41a.m. every morning. Cycling to the station from home takes the student on average 14 minutes, with a standard deviation of 3 minutes. You can assume that the distribution of trip times is normally distributed and independent between days. i) What is the probability that the student's cycle ride to the station will take more than 21 minutes? [4 marks] ii) If the student leaves the house at 8:22a.m. what percentage of the time will the student be late to university? [4 marks] iii) Conversely, at what time does the student have to leave their home so that missing the train will be unlikely (i.e. happening for at most 0.5% of all trips)? [4 marks] iv) Find the probability that two or more of the five cycling trips to the station per week will take 19 minutes or longer. [4 marks] v) Find the probability that, by leaving the house at 8:22a.m. every day, the student never misses the train in a whole month (= 20 weekdays). [4 marks]