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 feet (84 inches) with a standard deviation of 0.5 inch Assume the lengths are normally distributed You randomly select 35 boards and find that the mean length is 84.13 inches. Complete parts (a) through (c). Click the icon to view page 1 of the standard normal table, III 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 84.13 inches or more? 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 the sample mean be considered unusual because, if the seller's claim is true, the probability of obtaining this sample mean is (c) Ansuring the seller's claim is true, would it be unusual to have an individual board with a length of 84.13 inches? Why or why not? becane 84.13 within 2 standard deviations of the mean for an individual board Enter your answer in the answer box

Answer 1

- U solution Here a Griven mean (M)=8u in, n=35 5.D(0)=8.5 in a) Plā > 8.13)=P(2> 84-1384) 1:2= 0.5/538 ) =P(2>1.5382) = 1-P12515382) - 0.938 = 50.0620 b) The seller's claim appears to be accurate. The sample mani unusual because, if the seller's should not be considered claim is true, the probability of obtaining the sample mean is greater than 5% Assuming the Here p (7384113) = 0.0620 >0.05 So this not unusual. with in 25.Dls of the mean NO] because 84.13 is for an individual board. here 2-value = 1.5382 is with t2 Sid's