The lengths of lumber a machine cuts are normally distributed with a mean of 99 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 99.17 inches? (b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 99.17 inches?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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The lengths of lumber a machine cuts are normally distributed with a mean of 99 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 99.17 inches?
(b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 99.17 inches?
(a) The probability is.
(Round to four decimal places as needed.)
(b) 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 99 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 99.17 inches? (b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 99.17 inches? (a) The probability is. (Round to four decimal places as needed.) (b) The probability is- (Round to four decimal places as needed.)
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