The lengths of lumber a machine cuts are normally distributed with a mean of 100 inches and a standard deviation of 0.5 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 100.12 inches? (b) A sample of 40 boards is randomly selected. What is the probability that their mean length is greater than 100.12 inches? . .. .. (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.)