The lengths of lumber a machine cuts are normally distributed with a mean of 96 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the...

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Extracted text: The lengths of lumber a machine cuts are normally distributed with a mean of 96 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 96.32 inches? (b) A sample of 38 boards is randomly selected. What is the probability that their mean length is greater than 96.32 inches? (a) The probability is . (Round to four decimal places as needed.) (b) The probability is. (Round to four decimal places as needed.)