3. (a) Machine A produces metal pieces that are cylindrical in shape. The diameter of the metal pieces are normally distributed with mean 3.6 centimeters and a standard deviation of 0.3 centimeter. Suppose that a metal piece is considered as defective if its diameter is below 3.45 centimeter or exceeds 3.85 centimeter. Find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective metal pieces. (b) Suppose that, on average, Anthony's smartphone receives 6 messages per hour. [6 marks] (i) Assume a is the last digital number of your student id number (for example, your student number is 20987654D, then a = 4). Determine the probability that at least a messages will be received in the next 30 minutes. [4 marks] (ii) In a two hours exam, if 8 messages have been received, what is the probability that 2 messages have been received in the first 30 minutes? [5 marks] (c) During the NBA playoffs, Team X needs to win 3 matches over other teams in order to get to the championship match. In order for Team X to win a match over another Team Y, Team X needs to win best 4 out of 7 games in a match with the opposing team. Suppose there is a 0.53 probability Team X to win any game. What is the probability that Team X can get to the championship match? [5 marks] For 3b(i). a = 2