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 8 feet (96 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 96, 11 inches. Complete parts (a) through (c). EB Click the icon to view page 1 of the standard normal table EB 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 96 11 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 claim is true, the probability of obtaining this sample mean is (c) Assuming the seller's claim is true, would it be unusual to have an individual board with a length of 96 11 inches? Why or V The sample mean ▼ | be considered unusual because, if the seller's why not? because 96.11 within 2 standard deviations of the mean for an individual board

Answer 1

In a z normal distribution we have z= (x-u)/(sigma/sqrt (n))

Let find z value and then find p (z$\bg_white \geq$z0) , if p value is <0.05 then it is unusual and claim is accurate.

If z value is >2 then claim is true.

Given data are Population mean, 46 inche Population Sdo.b incb Sample, 4 Sample mean, 4 6.11 inches dtrn 、Z= 96, 11-91 0. 6 4-구 0,08子S 2 L1.26) = 1-0.8962 ,10-1038 -The Seless claim af poos to be (tv) accusata neample mean shoedd ocon sd ened unuva to be accusat The id ehed unuva be Selle's clain ts tvue then the pob ability is

less than 5 tht moan Po an ndividual boar d