Body mass index BMI is defined as BMI Weightheight2 measure

Body mass index (BMI) is defined as BMI = Weight/height^2 measured in kg / meter^2, A study by National Center for health statistics suggested that women between ages of 20 and 29 in the United states have a mean BMI of 26.8 with a standard deviation of 7.4. Let us assume that these BMIs are normally distributed. A BMI of 30 or greater is classified as being overweight. What proportion of women in this age range are overweight according to this definition

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    30      
u = mean =    26.8      
          
s = standard deviation =    7.4      
          
Thus,          
          
z = (x - u) / s =    0.432432432      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.432432432   ) =    0.332713575 [answer]