Your lumber company has bought a machine that automatically cuts lumber. The sel
ID: 3061021 • Letter: Y
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 6 feet ( 72 72 inches) with a standard deviation of 0.5 0.5 inch. Assume the lengths are normally distributed. You randomly select 43 43 boards and find that the mean length is 72.22 72.22 inches. Complete parts (a) through (c). LOADING... Click the icon to view page 1 of the standard normal table. LOADING... 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 72.22 72.22 inches or more? nothing (Round to four decimal places as needed.) (b) Using your answer from part (a), what do you think of the seller's claim? The seller's claim appears to be inaccurate. accurate. The sample mean should should not be considered unusual because, if the seller's claim is true, the probability of obtaining this sample mean is greater than 10%. greater than 5%. less than 10%. less than 5%. (c) Assuming the seller's claim is true, would it be unusual to have an individual board with a length of 72.22 72.22 inches? Why or why not? No, Yes, because 72.22 72.22 is not is within 2 standard deviations of the mean for an individual board.
Explanation / Answer
Mean length = 72 inches ( 6 feet )
Std dev = 0.5 inch
n = 43
sample mean = 72.22 inches
A)
Z score = ( Sample mean - true mean ) / (std dev / sqrt(n))
= (72.22 - 72) / (0.5/sqrt(43))
= 2.8871
P(X>=72.22) = 1 - P(X < 72.22) = 1 - P(Z = 2.8871) =10.9981=0.0019
Thus the probability that the mean of the sample is 72.21 inches or more is 0.0019
B) The seller's claims are inaccurate because of such a small probability as obtained above
c) Sample mean should be not be considered unusual since it falls within 2 std deviation from the mean (<72+2*0.5)
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