Please provide detailed explanations Your body mass index BM

Please provide detailed explanations

Your body mass index (BMI) is your weight in kilograms divided by the square of your height in meters. Many online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of overweight or obesity. 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 6.3

1/ People with BMI less than 19.1 are often classified as \" underweight.\"

What percent (±0.01) of young women are under-weight by this criterion?  %

2/ People with BMI over 31 are often classified as \" obese.\"

What percent (±0.01) of young women are obese by this criterion?

Solution

1)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    19.1      
u = mean =    26.5      
          
s = standard deviation =    6.3      
          
Thus,          
          
z = (x - u) / s =    -1.174603175      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -1.174603175   ) =    0.120076756

= 12.01% [answer]

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2)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    31      
u = mean =    26.5      
          
s = standard deviation =    6.3      
          
Thus,          
          
z = (x - u) / s =    0.714285714      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.714285714   ) =    0.237525262

= 23.75% [answer]