Concept explainers
(a)
To find: the percentile of the soldier's head circumference
(a)
Answer to Problem 12PT
Thesoldier's head circumference is in approximately the 84th percentile.
Explanation of Solution
Given:
Mean,
Standard deviation,
Calculation:
By definitions, the 2-score that corresponds to the soldier whose head circumference is 23.9 inches is given as follows:
Using standard normal tables, we observe the proportion corresponding to the score z = 1 as 0.8413. That means that this soldier's head circumference is in approximately the 84th percentile. This is shown in the below graph.
Conclusion:
Therefore, the soldier's head circumference is in approximately the 84th percentile.
(b)
To find: percent of male soldiers who require custom helmets
(b)
Answer to Problem 12PT
Approximately 0.7% of soldiers require a customized helmet order.
Explanation of Solution
Calculation:
The army's helmet supplier regularly stocks helmets that fit male soldiers with head circumferences between 20 and 26 inches. Anyone with a head circumference outside that interval requires a customized helmet order.
By definitions, the Z-score that corresponds to the soldier whose head circumference is 20 inches is given as follows:
By definitions, the Z-score that corresponds to the soldier whose head circumference is 20 inches is given as follows:
Using standard normal tables, we observe the proportion corresponding to the score
This means that the area in both tails is:
Therefore approximately 0.7% of soldiers require a customized helmet order.
Conclusion:
Therefore approximately 0.7% of soldiers require a customized helmet order.
(c)
To find: the
(c)
Answer to Problem 12PT
Interquartile
Explanation of Solution
Calculation:
The
This means that
So,
Conclusion:
Therefore, the interquartile range is 1.474 inches.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
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