In large-scale tree-felling operations, a machine cuts down trees, strips off the branches and then cuts the trunks into logs of length X feet for transporting to a sawmill.
It may be assumed that values of X are normally distributed with mean = 3 feet and a
standard deviation of 0.50 feet.
A cut log is randomly selected. Calculate the following probabilities. Round your final
answers to four decimal places.
(a) The log is less than 2 feet
(b) The log is exactly 3.5 feet
(c) The log is between 2 and 5 feet
(d) The log is more than 3.5 feet
(e) The log is either more than 3.5 feet or less than 2 feet
(f) Log lengths in the top 10% of the distribution are deemed a driving hazard. What is the
shortest log length that would deem a log a driving hazard?
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