Suppose you are out fishing and you want to predict the amount of time (in minutes) it takes to catch 3 fish. Let (15,10) be the time it takes to reel in a fish. Let (10,8) be the amount of time you spend waiting for the fish to take the bait. Assume TF and TT are independent. Also assume you start timing as soon as you start reeling in the first fish, and the time ends when you have finished catching the third fish.

a) Let T be the random variable for the total amount of time spent fishing. What is E[T] and Var[T]? Save your variables as exp.T and var.T. (Hint: Note that a variance of 122 is incorrect for this problem. Why? If Z1 and Z2 are indepedent N(0,1) random variables, the distribution of Z1+Z2 is not the same as 2Z1. If you want to explore this, you can run some simulations to see for yourself.)

b) What is the probability that you finish catching the three fish in 60 minutes or less? Round your answer to three decimal places. Save your answer as p2.2.