The lengths of lumber a machine cuts are normally distributed with a mean of 101 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 101.17 ​inches? ​(b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 101.17 ​inches?       ​(a) The probability is ____. ​(Round to four decimal places as​ needed.) ​(b) The probability is ____. ​(Round to four decimal places as​ needed

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