Question 2 Given the following probability distribution of Z, 1 2 0 < x < 60 f(z) = 30 1800 otherwise ~ If Zi (z,o) and Z is the sample mean:(2;10;4) (a) Find an expression in terms of n, z and oz for E(Z2). Show working. (b) Using the given probability distribution, if n = 50, find a numerical solution. (c) Assume there are 50 marathon runners, each with a finishing time in minutes. Let's say Z; represents the time it takes for runner i to finish the marathon. Assume each runner's finishing time is independent and has the probability distribution f(z) given above. If Z is how long it takes, on average, for the runners to finish the marathon, what is the probability that, on average, a runner's finishing time is less than 30 minutes during the event, using the central limit theorem and the results from part (b)? From the text (5th edition)