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 92.14 inches? (b) A sample of 40 boards is randomly selected. What is the probability that their mean length is greater than 92.14 inches? (a) The probability is

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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The lengths of lumber a machine cuts are normally distributed with a mean of 92 inches and a standard devlation of 0.5 inch.
(a) What is the probability that a randomly selected board cut by the machine has a length greater than 92.14 inches?
(b) A sample of 40 boards is randomly selected. What is the probability that their mean length is greater than 92.14 inches?
(a) The probability is
(Round to four decimal places as needed.)
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Transcribed Image Text:The lengths of lumber a machine cuts are normally distributed with a mean of 92 inches and a standard devlation of 0.5 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 92.14 inches? (b) A sample of 40 boards is randomly selected. What is the probability that their mean length is greater than 92.14 inches? (a) The probability is (Round to four decimal places as needed.) Enter your answer in the answer box and then cick Check Answer part remaining
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