The lengths of lumber a machine cuts are normally distributed with a mean of 93 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 93.13 inches? (b) A sample of 40 boards is randomly selected. What is the probability that their mean length is greater than 93.13 inches? (a) The probability is u25fb. (Round to four decimal places as needed.) (b) The probability is u25fb. (Round to four decimal places as needed.)
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Step 1
First, we need to find the z-score for a single board with a length of 93.13 inches. The z-score formula is: z = (X - μ) / σ where X is the value we're interested in (93.13 inches), μ is the mean (93 inches), and σ is the standard deviation (0.4 inch). Show more…
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