Question 1 Assume that it is known that the departure delay time (in hours) of flights leaving from New York has a mean delay time of 12 hours and a standard deviation of 40 hours. Thus, 75% of flights have a departure delay time of less than 11 hours. a. Does the distribution of departure delay time follow a Normal distribution? Briefly explain your answer. [3 marks] b. Suppose we want to know the probability that a randomly selected flight will depart more than 12 hours late. Can we find this probability? If so, calculate the probability. If not, briefly explain why we cannot. [2 marks] c. Suppose we want to know the probability that the average departure delay time of 5 randomly selected flights will be more than 12 hours late. Can we find this probability? If so, calculate the probability. If not, briefly explain why we cannot. [2 marks d. Suppose we want to know the probability that the average departure delay time of 50 randomly selected flights will be more than 12 hours late. Can we find this probability? If so, calculate the probability. If not, briefly explain why we cannot. [3 marks] e. Suppose we want to know the probability that the average departure delay time of 50 randomly selected flights will be more than 18 hours late. Can we find this probability? If so, calculate the probability. If not, briefly explain why we cannot. [3 marks]