The lengths of lumber a machine cuts are normally distributed with a mean of 98 inches and a standard deviation of 0.3 inch.

(a) What is the probability that a randomly selected board cut by the machine has a length greater than 98.11 inches?

(b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 98.11 inches?

_____________________________________

(a) The probability is :

(Round to four decimal places asneeded.)

(b) The probability is :

(Round to four decimal places asneeded.)