(Solved): The lengths of lumber a machine cuts are normally distributed with a mean of 97 inches and a standar ...

The lengths of lumber a machine cuts are normally distributed with a mean of 97 inches and a standard deviation of 0.6 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 97.22 inches? (b) A sample of 40 boards is randomly selected. What is the probability that their mean length is greater than 97.22 inches? (a) The probability is (Round to four decimal places as needed.)