(Solved): The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distri ...

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 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2 decimal places) that the sum of the 95 wait times you observed is between 536 and \( 637 ? \) Part b) What is the approximate probability (to 2 decimal places) that the average of the 95 wait times exceeds 6 minutes? Part c) Find the probability (to 2 decimal places) that 92 or more of the 95 wait times exceed 1 minute. Piease 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 95 wait times recorded exceed 5 minutes: