STAT 1000 Question 4 (4 points) A student must pass through 12 sets of traffic lights on his way to university. Suppose that each of the lights is green 35.7% of the time, yellow 5.4% of the time, and red 58.9% of the time. Suppose also that the traffic lights function independently. (a) Let X be the number of red lights encountered by the student on his way to university. Find the mean and variance of X. (b) What is the probability that the student encounters exactly five red lights on his way to university one day? (c) What is the probability that the student encounters at least three green lights on his way to university one day? (d) In a five-day school week, what is the probability that the student encounters exactly six yellow lights on his way to university?