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 9 feet (108 inches) with a standard deviation of 0.4 inch. Assume the lengths are normally distributed. You randomly select 44 boards and find that the mean length is 108.15 inches. Complete part(a) through(c). (a) Assuming the seller's claim is correct what is the probability that the mean of the sample is 108.15 inches or more? (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 because, if the seller's 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 bond with a length of 108.15 inches? Why or why not?

Explanation / Answer

x = 108.15 in
µ = 108 in
= 0.4 in
n = 44
````````````

z = (x - µ) / s

s is given by
s = /n
where s is the sample standard deviation,

s = 0.4/44

z = (108.15 - 108) / (0.4/44 ) = 2.49

from z-index table
P(x < 108.15) = P(z = 2.49) = 0.9936

P(108.15 or more) 1 - P(x < 108.15) = 1 -0.9936= 0.0064

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