Question

PLEASE ONLY ANSWER E AND F

A forester measured a sample of trees in a tract of land being sold for a lumber harvest. Among 27 trees, she found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose her sample gives an accurate representation of the entire tract of land and that the tree diameters follow a normal distribution. Round to 2 decimal places, when applicable.

(a) Sketch a graph of the distribution of tree diameters, labeling the mean and one standard deviation in either direction.

(b) What diameter would you expect the central 95% of trees to be?

(c) What percentage of trees should be less than 1 inch in diameter?

(d) What percentage of trees should be between 10.4 and 19.8 inches in diameter?

(e) What is the minimum diameter a tree can have in order to be placed in the top 5% of all such trees on the tract regarding their size?

(f) Suppose the forester looked at another tract of land and found that those tree’s diameters also followed a normal distribution with a mean diameter of 12.3 inches with a standard deviation of 2.25 inches. Would it be more unusual to find a tree with a diameter of 15 inches in the first tract of land described or in the second one described in this part? Hint: use z-scores. You must support your work mathematically for full credit, simply saying “1^st tract” or “2^nd tract” is not sufficient.

Answer 1

E) minimum diameter is 18.13 inches

F) second track is more unusual

Note: a diameter said to be unusual only when it's Z score is more than 2 or less than-2