Engineers Initially Surveyed the Territory of Iowa in the 1830 $15 , " 1 \mathrm {~s} \mid "$

question 8

Essay

Engineers initially surveyed the Territory of Iowa in the 1830 's, and they were very careful to take note of the trees and vegetation. The sample of Ash tree diameters from the original survey of what is now Linn County is presented in the stem-and-leaf display below. The display uses five lines for each stem. Thus, "1t|" is the stem for diameters of 12 and 13 , "1f|" for 14 and $15 , " 1 \mathrm {~s} \mid "$ for 16 and 17 , and so on. (The "t" then stands for leaves that are twos and threes, the " $f$ " for leaves of fours and fives, etc.)
The mean diameter of the 102 ash trees in this sample is $11.500$ inches, and the standard deviation is $3.842$ inches. Linn County Trees in 1830
Ash Diameters $1 \mid 0 = 10$ inches $\quad \mathrm { N } = 102$
$0 . \mid$
ot $\mid 2$
of $\mid 44$
os $\mid 666777$
$0 * \mid 8888888888888888888999$
$1 . \mid 000000000000000000$
$1 t \mid 22222222222222222222222$
$1 f \mid 444444444445$
$1 s \mid 666666$
$1 * \mid 8888888888$
$2 \cdot \mid 0$
$2 t \mid$
$2 f \mid 4$
$2 s \mid$
$2 * \mid$ (a) What is the approximate diameter of an ash tree at the 20th percentile in this
distribution?
(b) According to the Empirical Rule, approximately 68% of ash tree diameters are
between what two values?

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Definitions:

Bipolar Cell

A type of neuron found in the eyes that conducts signals from the photoreceptors to the ganglion cells, integral in the visual pathway.

Cone

(1) In botany, a reproductive structure in many gymnosperms that produces either microspores or megaspores. (2) In zoology, one of the conical photoreceptive cells of the retina that is particularly sensitive to bright light and, by distinguishing light of various wavelengths, mediates color vision. Compare with rod.

Compound Eye

A type of eye found in some arthropods, consisting of multiple small visual units that provide a wide field of vision and the ability to detect movement.

Camera Eye

A type of eye found in vertebrates and some mollusks that is characterized by a spherical lens that focuses light on the retina, producing a detailed image.