Question

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.

Answer 1

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