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Solved: The waist circumference of males 20 to 29 years
Chapter 7, Problem 7CT(choose chapter or problem)
Problem 7CT
The waist circumference of males 20 to 29 years old is approximately normally distributed, with mean 92.5 cm and standard deviation 13.7 cm.
Source: M. A. McDowell, C. D. Fryar, R. Hirsch, and C. L. Ogden. Anthropometric Reference Data for Children and Adults: U. S. Population, 1999–2002. Advance data from vital and health statistics: No. 361. Hyattsville, MD: National Center for Health Statistics, 2005.
(a) Use the normal model to determine the proportion of 20- to 29-year-old males whose waist circumference is less than 100 cm.
(b) What is the probability that a randomly selected 20- to 29- year-old male has a waist circumference between 80 and 100 cm?
(c) Determine the waist circumferences that represent the middle 90% of all waist circumferences.
(d) Determine the waist circumference that is at the 10th percentile.
Questions & Answers
QUESTION:
Problem 7CT
The waist circumference of males 20 to 29 years old is approximately normally distributed, with mean 92.5 cm and standard deviation 13.7 cm.
Source: M. A. McDowell, C. D. Fryar, R. Hirsch, and C. L. Ogden. Anthropometric Reference Data for Children and Adults: U. S. Population, 1999–2002. Advance data from vital and health statistics: No. 361. Hyattsville, MD: National Center for Health Statistics, 2005.
(a) Use the normal model to determine the proportion of 20- to 29-year-old males whose waist circumference is less than 100 cm.
(b) What is the probability that a randomly selected 20- to 29- year-old male has a waist circumference between 80 and 100 cm?
(c) Determine the waist circumferences that represent the middle 90% of all waist circumferences.
(d) Determine the waist circumference that is at the 10th percentile.
ANSWER:
Answer:
Step 1 of 2
The waist circumference of males 20 to 29 years old is approximately normally distributed, with mean 92.5 cm and standard deviation 13.7 cm.
(a) Use the normal model to determine the proportion of 20- to 29-year-old males whose waist circumference is less than 100 cm.
Given, P(X < 100)
P(= P(Z < 0.5474
)
Now, P( Z < 0.55) = 0.7088 (From Area Under Normal Curve table)
(b) The probability that a randomly selected 20- to 29- year-old male has a waist circumference between 80 and 100 cm
P(= P(-0.91 < Z < 0.55)
P( Z < 0.55) - P( Z > -0.91) = 0.7088 - 0.1814 (from area under normal curve table)
= 0.5274