(Solved): A subway train arrives every six minutes during rush hour. We are interested in the length of time ...

A subway train arrives every six minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. Round your answer to four decimal places where possible. Don't forget to show your work. a. (5 pts) Find the mean of this distribution. b. (5 pts) Find the standard deviation of this distribution. You will find the probability that a commuter will wait between \( 3.3 \) and \( 5.5 \) minutes for a train. c. (5 pts) Sketch the distribution function AND shade the area under the curve which is between \( 3.3 \) and \( 5.5 \) minutes. d. (5 pts) Now use Part c to find the probability of a commuter waiting between \( 3.3 \) and \( 5.5 \) minutes for a train.