. Your lumber company has bought a machine that automatically cuts lumber. The s
ID: 3263944 • Letter: #
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 ft. (96 in. ) with a standard deviation of 0.5 inch. Assume the lengths are normally distributed. You randomly select 40 boards and find that the mean length is 96.25 inches.
a) What is the probability that the mean of the sample is 96.25 inches or more?
b) Would it be unusual to have an individual board with a length of 96.25 inches? Why or why not?
Explanation / Answer
Answer to the question as follows:
Mean length = 8ft
Standard deviation = 0.5ft
n = 40, Sample mean = 96.25 inches
a. P(X>=96.25) = P(Z> = (96.25-96)(6/sqrt(40)) = P(Z>= 0.24) = 1-0.5948 = .4052
b. No it is not unusual to have an individual board with a length of 96.25 inches. This is because the probability of having length greater than 96.25 itself is .4052 which is not small, it's a huge probability
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