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Part 1

The lengths of lumber a machine cuts are normally distributed with a mean of

92

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

92.12

inches?

(b) A sample of

41

boards is randomly selected. What is the probability that their mean length is greater than

92.12

inches?

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Part 1

(a) The probability is

enter your response here.

(Round to four decimal places as needed.)

Part 2

(b) The probability is

enter your response here.

(Round to four decimal places as needed.)