The lengths of lumber a machine cuts are normally distributedwith a mean of 99 inches and a standard deviation of 0.5 inch. ​(a)What is the probability that a randomly selected board cut by themachine has a length greater than 99.11 ​inches? ​(b) A sample of44 boards is randomly selected. What is the probability that theirmean length is greater than 99.11 ​inches?