The lengths of lumber a machine cuts are normally distributed with a mean of 89 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 89.15 inches?

(b) A sample of 44 boards is randomly selected. What is the probability that their mean length is greater than 89.15 inches?

(a) The probability is

nothing

.

(Round to four decimal places asneeded.)

(b) The probability is

nothing

.