Dr. Hu is training for the Boston Marathon. Based on online research, Dr. Hu found out that there were 24,607 runners who finished last year (2022) with an average finish time of 3 hours 45 mins (225 mins) and a standard deviation of 60 mins. Dr. Hu's personal best is 2 hours 45 mins (165 mins). Assume this year there will be 25,000 runners participating in the Boston Marathon. Assume the average performance of the runners will improve by 5 mins (220 mins) with the same standard deviation (60 mins), and the data will still be normally distributed. To finish as one of the first 500 runners, What is the maximum time Dr. Hu can take to complete the marathon?
