The lengths of lumber a machine cuts are normally distributed with a mean of 101 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 101.22 inches? (b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 101.22 inches? (a) The probability is. (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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The lengths of lumber a machine cuts are normally distributed with a mean of 101 inches and a standard deviation of 0.7 inch.
(a) What is the probability that a randomly selected board cut by the machine has a length greater than 101.22 inches?
(b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 101.22 inches?
(a) The probability is.
(Round to four decimal places as needed.)
Transcribed Image Text:The lengths of lumber a machine cuts are normally distributed with a mean of 101 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 101.22 inches? (b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 101.22 inches? (a) The probability is. (Round to four decimal places as needed.)
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