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. 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 95 wait times recorded exceed 5 minutes.
The Attempt at a Solution
I know that for part c and d I need to use binomial distribution, however I am unsure of what to do for part a and b
What I tried for a was ((637/95)-(536/95))/12 and for b I thought I could just do 7/12 since it is uniformly distributed, but neither are correct. Can anyone tell me if there is a certain formula to follow? Or what I am doing wrong? Thanks[/B]