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 7 feet (84 inches) with a standard deviation of 0.7 inch. Assume the lengths are normally distributed. You randomly select 42 boards and find that the mean length is 84.25 inches. (a) Assuming the seller's claim is correct, what is the probability that the mean of the sample is 84.25 inches or more? ____ (Round to four decimal places as needed.)

Explanation / Answer

Mean ( u ) = 84
Standard Deviation ( sd )=0.7
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X < 84.25) = (84.25-84)/0.7
= 0.25/0.7= 0.3571
= P ( Z <0.3571) From Standard Normal Table
= 0.6395                  
P(X > = 84.25) = (1 - P(X < 84.25)
= 1 - 0.6395 = 0.3605                  

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