Statistics Through Applications
Statistics Through Applications
2nd Edition
ISBN: 9781429219747
Author: Daren S. Starnes, David Moore, Dan Yates
Publisher: Macmillan Higher Education
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Chapter 3, Problem 3.54RE
To determine

To find: the head size gets custom-made helmets.

Expert Solution & Answer
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Answer to Problem 3.54RE

Head circumference of less than 19.965 inches or more than 24.6095 inches

Explanation of Solution

Given:

  μ=22.8inchesσ=1.1inches

Formula used:

  z=xμσ

Calculation:

Probability of 5% = 0.05 and 95% =0.95

Z-score for corresponding to 0.05 is -2.575

Z-score for corresponding to 0.95 is 1.645

For z = -2.575

  z=xμσ2.575=x22.81.12.8325=x22.8x=19.9675

For z= 1.645

  z=xμσ1.645=x22.81.11.8095=x22.8x=24.6095

Therefore the soldiers who have a head circumference of less than 19.965 inches or more than 24.6095 inches get a custom-made helmet.

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