The duration spent by Miss Jenny to bake a swissroll is normally distributed with a mean of 45 minutes and a standard deviation of 15 minutes. Miss Jenny booked Lalarun service to deliver her swissroll to customer once she starts baking. Lalarun service will be at Miss Jenny place in 50 minutes time. (i) What is the probability that the Lalarun rider will have to wait before the swissroll is passed to him? (5 marks)

(ii) What is the percentage that the swissroll will be done between 40 to 50 minutes? (5 marks)

(iii) Given that 90% of the swissroll can be done in less than k minutes, find the value of k. (5 marks)

(iv) Given that the swissroll will be done in less than 40 minutes. Five swissrolls baked by Miss Jenny were selected, what is the probability that at most 2 were done in less than 40 minutes? (10 marks)