A study by the National Center for Health Statistics found that the BMI of American young women (ages 20 to 29) is approximately Normal with mean 26.5 and standard deviation 6.4.10

(a) People with BMI less than 18.5 are often classified as “underweight.” What percent of young women are underweight by this criterion?

(b) People with BMI over 30 are often classified as “obese.” What percent of young women are obese by this criterion?

Question

A study by the National Center for Health Statistics found that the BMI of American young women (ages 20 to 29) is approximately Normal with mean 26.5 and standard deviation 6.4.10

(a) People with BMI less than 18.5 are often classified as “underweight.” What percent of young women are underweight by this criterion?
 
(b) People with BMI over 30 are often classified as “obese.” What percent of young women are obese by this criterion?

mathmate · Answer

Use the normal distribution table.

mathmate · Answer

|dw:1423505184673:dw|
Z(X)=(X-$\mu$)/$\sigma$
and the entry of the table is the probability that x<X
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Example: to find the percentage (interpreted as probability) of people with BMI under 15?
Z(15)=(15-26)/6.410=-1.716
The normal distribution table gives P(z<-1.716)= 0.0431, or 4.3% of people have BMI=15 or less.
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