Question: 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

In large-scale tree-felling operations, a machine cuts down trees, strips off the branches and then cuts the trunks into logs of lengthXfeet for transporting to a sawmill.

It may be assumed that values ofXare normally distributed with mean = 3 feet and a standard deviationof 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

(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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