The lengths of lumber a machine cuts are normally distributed with a mean of 97 inches and a standard deviation of 0.6 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 97.28 inches? (b) A sample of 37 boards is randomly selected. What is the probability that their mean length is greater than 97.28 inches? (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.) M www

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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The lengths of lumber a machine cuts are normally distributed with a mean of 97 inches and a standard deviation of 0.6 inch.
(a) What is the probability that a randomly selected board cut by the machine has a length greater than 97.28 inches?
(b) A sample of 37 boards is randomly selected. What is the probability that their mean length is greater than 97.28 inches?
(a) The probability is
(Round to four decimal places as needed.)
(b) The probability is
(Round to four decimal places as needed.)
B
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Transcribed Image Text:The lengths of lumber a machine cuts are normally distributed with a mean of 97 inches and a standard deviation of 0.6 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 97.28 inches? (b) A sample of 37 boards is randomly selected. What is the probability that their mean length is greater than 97.28 inches? (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.) B www
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