Suppose you have a tree farm and you have 1000 live oaks on this farm. You are w

Question

Suppose you have a tree farm and you have 1000 live oaks on this farm. You are wondering if this would be a profitable time to harvest the tallest ones – those over 55 feet tall. Your sample of 100 of them indicates that their average height is 45 feet and that the standard deviation (s) of their heights is 5 feet. How many trees in your farm to you predict will have a height greater than 55 feet? (For this answer you do not need to provide a written explanation – simply provide the final answer and show enough of your work to earn part credit if your final answer is wrong. If you can simply provide a written explanation of your math that will be acceptable too.) Suppose you have a tree farm and you have 1000 live oaks on this farm. You are wondering if this would be a profitable time to harvest the tallest ones – those over 55 feet tall. Your sample of 100 of them indicates that their average height is 45 feet and that the standard deviation (s) of their heights is 5 feet. How many trees in your farm to you predict will have a height greater than 55 feet? (For this answer you do not need to provide a written explanation – simply provide the final answer and show enough of your work to earn part credit if your final answer is wrong. If you can simply provide a written explanation of your math that will be acceptable too.)

Explanation / Answer

P(X > 55) = P((X - mean)/sd) > (55 - mean)/sd)

               = P(Z > (55 - 45)/5)

               = P(Z > 2)

               = 1 - P(Z < 2)

               = 1 - 0.9772 = 0.0228

The no of trees have a height greater than 55 = 0.0228 * 1000 = 22.8 = 23

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