Question

The BMI pf American men between ages 30 and 50 is normally distributed with a mean of 27.2 and a standard deviation of 5.1

Determine the z-score and percentile of a BMI of 30?

If an American male belonged to a BMI percentile of 40% what would be his z score?

If a BMI of 25 or greater signifies overweight and a BMI of 30 or greater signifies obese what precentage of Americans are overweight? obese?

Answer 1

Let X denote the BMI of these American men. Then .

The z score is obtained for a value by first deducting the mean from it and then dividing it by the standard deviation.

The z-score of a BMI of 30 is:

                                         

Let his z-score be x. Then if an American male belongs to the 40% percentile we have:

                                            

We can look this up in a table or use a calculator. This gives x=-0.253.

The percentage of Americans that are overweight are given by

                       

Thus, the required percentage of overweight American men is: 66.69%

The percentage of Americans that are obese are given by

                       

Thus, the required percentage of overweight American men is: 29.15%