Question 4 (13 marks): A health club lets members use, on each visit, its facilities for as long as they wish. The club's records suggest that the length of a visit can be modeled by a Normal distribution with mean 90 minutes. Only 20% of members stay for more than 125 minutes. a) (3 marks) Find the standard deviation of the normal distribution. b) (2 marks) Find the probability that a visit lasts less than 25 minutes. c) (3 marks) Find the probability that a visit lasts between 60 and 120 minutes. (1) (3 marks) Two members arrive at the club and each stay a time that is independent of the other. Find the probability that one member stays more than 60 minutes and the other member stays less than 25 minutes. e) (2 marks) Due to regional restrictions imposed the health club needs to adjust the average time spent such that 90% of members stay for less than 90 minutes. Assuming the standard deviation remains the same as that solved for in part a), find the new mean average time spent in the health club