The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 100 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2 decimal places) that the sum of the 100 wait times you observed is between 565 and 669 ?
Part b) What is the approximate probability (to 2 decimal places) that the average of the 100 wait times exceeds 6 minutes?
Part c) Find the probability (to 2 decimal places) that 97 or more of the 100 wait times exceed 1 minute. Please carry answers to at least 6 decimal places in intermediate steps.
Part d) Use the Normal approximation to the Binomial distribution (with continuity correction) to find the probability (to 2 decimal places) that 56 or more of the 100 wait times recorded exceed 5 minutes.