T. A. tunnel opens at Tam and on average 27 red trucks enter this tunnel from Tam to 10am on Monday mornings. Suppose the red trucks arrive independent of each other and at a constant rate. {a} {1 point] Let X be the number of red trucks that pass through the tunnel between Tam and larn over the next Monday. What is the distribution of X? {b} {2 points] Again let X be the number of red trucks that pass through the tunnel between Tam and lam next Monday. How many red trucks would you expect to pass through the tunnel between Tara and larn next Monday? (c) {5 points] 'Wl'iat is the probability that 8 red trucks pass through the tunnel between 8am and 9am? State the appropriate distribution and any parameter values for any random variable(s} you use to model the situation. Write the probability statement and show your work in order to solve the problem. [:1] {=1 points] Suppose it takes a half hour for a red truck to pass through the tunnel. If there are no red trucks in the tunnel when it enters the tunnel at 7:35am on a Monday, what is the probability it will be the only red truck in the tunnel the whole time it spends in the tunnel? State the appropriate distribution and any parameter values for any random variable{s]| you use to model the situation. Write the probability statment and show your work to receive full credit. [e] {5 points] Let W represent the amount of time in hours it takes for the 9\"\" red truck to arrive at the tunnel on a Monday morning. What time do you expect the 9\"" red truck to arrive at the tunnel on a Monday morning {to the nearest 1!] minutes}? Recall the tunnel opens at Tam. Your nal answer should be a time