Your lumber company has bought a machine that automatically cuts lumber. The sel
ID: 3061499 • 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 7 7 feet ( 84 84 inches) with a standard deviation of 0.6 0.6 inch. Assume the lengths are normally distributed. You randomly select 47 47 boards and find that the mean length is 84.23 84.23 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 84.23 84.23 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 accurate. inaccurate. The sample mean should not should be considered unusual because, if the seller's claim is true, the probability of obtaining this sample mean is greater than 5%. less than 5%. greater than 10%. less than 10%. (c) Assuming the seller's claim is true, would it be unusual to have an individual board with a length of 84.23 84.23 inches? Why or why not? No, Yes, because 84.23 84.23 is is not within 2 standard deviations of the mean for an individual board.
Explanation / Answer
a)
probability that the mean of the sample is 84.23 inches or more:
The seller's claim appears to be inaccurate. The sample mean should be considered unusual because, if the seller's claim is true, the probability of obtaining this sample mean is less than 5%.
c) Yes, because 84.23 is not within 2 standard deviations of the mean for an individual board.
for normal distribution z score =(X-)/ here mean= = 84 std deviation == 0.6000 sample size =n= 47 std error=x=/n= 0.0875Related Questions
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