Compare two runners and distinguish a sum from a multiple

The times taken by two runners A and B to run 400 metre races are independent and normally distributed with means 45.0 seconds and 45.2 seconds and standard deviation 0.5 seconds and 0.8 seconds respectively. The two runners are to compete in a 400 metre race for which there is a track record of 44.5 seconds.

(i) Calculate the probability of runner A breaking the track record. Hence, show that the probability of runner B breaking the record is greater than that of runner A.3 marks

(ii) Find the probability of runner A beating runner B.3 marks

(iii) Find the probability that the total sum of four randomly chosen times of A is more than 4 times a randomly chosen time of B.5 marks