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(Steps Shown) Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a

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 the mean length is 96.25 inches.

  1. What is the probability that the mean of the sample is 96.25 inches or more?
  2. Would it be unusual to have an individual board length of 96.25 inches? ____________ Why or why not ? SKETCH THE CURVE.

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