Your lumber company has bought a machine that automatically cuts lumber. The sel

Question

Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 6 feet (72 inches) with a standard deviation of 0.6 inch. Assume the lengths are normally distributed. You randomly select 47 boards and find that the mean length is 72.18 inches. Complete parts (a) through (c). 1. Click the icon to view page 1 of the standard normal table. 2. Click the icon to view page 2 of the standard normal table. (a) Assuming the seller's claim is correct, what is the probability that the mean of the sample is 72.18 inches or more? ______ (Round to four decimal places as needed.) (b) Using your answer from part (a), what do you think of the sellers claim? The seller's claim appears to be (1) _______ The sample mean (2) _____ be considered unusual because, if the sellers claim is true, the probability of obtaining this sample mean is (3) ______ (c) Assuming the sellers claim is true, would it be unusual to have an individual board with a length of 72.18 inches? Why why not? (4) ______ because 72.18 (5) _______ within 2 standard deviations of the mean for an individual board.

Explanation / Answer

(a) We will use z-dist:

excel formula:

(b) (1) True/valid/acceptable

(2) 72.18

(3) Very less i.e. less than 5%

(c)

(4) Given sample mean is unusual

(5) is not within

z= 2.056696 prob(length>72.18)= 1.9843%

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