The lengths of lumber a machine cuts are normally distributed with a mean of 99 inches and a standard deviation of 0.4 inch.​(a) What is the probability that a randomly selected board cut by the...

The lengths of lumber a machine cuts are normally distributed with a mean of 99 inches and a standard deviation of 0.4 inch. ​(a) What is the probability that a randomly selected board cut by the machine has a length greater than 99.13 ​inches? ​(b) A sample of 39 boards is randomly selected. What is the probability that their mean length is greater than 99.13 ​inches? ​(a) The probability is nothing. ​(Round to four decimal places as​ needed.) ​(b) The probability is nothing. ​(Round to four decimal places as​ needed.)