Making handcrafted pottery generally takes two major steps: wheel throwing and firing. That is, the time for a piece of pottery to be finished is the sum of the time associated with these two steps. The time for wheel throwing and the time for firing are each normally distributed random variables with means of 50 min and 70 min and standard deviations of 5 min and 7 min, respectively. That is, if we let the random variable X represent the time for wheel throwing, then X-N(50,25). Furthermore, if we let the random variable Y represent the time for firing, then Y-N(70,49). Part a (5 points): Assuming the time required for wheel throwing and firing are independent, what is the probability that a piece of pottery will be finished within 110 minutes? Part b (5 points): Let X, denote the wheel throwing time required for the i-th piece of pottery produced. Suppose X- N(50,25) for each and the X-variables are independent of each other. Let X denote the average wheel throwing time required by the first 5 pieces of pottery. What is P(