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

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?