The lengths of lumber a machine cuts are normally distributed with a mean of 106 inches and a standard deviation of 0.3 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 106.14 inches? (b) A sample of 39 boards is randomly selected. What is the probability that their mean length is greater than 106.14 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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14 inches. The z-score is calculated as: z = (X - μ) / σ where X is the value we're interested in, μ is the mean, and σ is the standard deviation. For part (a), we have: z = (106.14 - 106) / 0.3 = 0.14 / 0.3 ≈ 0.467 Now, we need to find the probability that a Show more…
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