Question

BMI (Body Mass Index) is your weight in kilograms divided by the square of your height in meters. BMI for women is approximately Normal with mean 26.8 and standard deviation 7.4;

1. If you wanted to classify the bottom 15% of all women as underweight and top 15% of all women as “obese” what BMI indices would you need to separate these two categories?

Answer 1

Solution:-

Given that,

mean = = 26.8

standard deviation = = 7.4

bottom 15% is

P(Z < z ) = 0.15

z = -1.036

Using z-score formula,

x = z * +

x =(-1.036) * 7.4 + 26.8

x = 19.13

Top 15% is

P(Z > z ) = 0.15

1- P(z < z) =0.15

P(z < z) = 1-0.15 = 0.85

z =1.036

Using z-score formula,

x = z * +

x = 1.036 * 7.4 + 26.8

x = 34.47