Question

A person is said to be overweight if his or her Body Mass Index is between 25 and 29, inclusive, and a person is said to be obese if his or her Body Mass Index is 30 or greater. In 2018, the Utah Department of Health issued the following table. The first two columns of the table provide the age distribution for adults living in Utah. The third column gives the percentage of adults in each age group who are either overweight or obese.

              Age                     % Adults            % Overweight or Obese

          18-34                         42.5                              41.1

          35-49                         28.5                              57.9

          50-64                         16.4                              68.2

          65&over                   12.6                              55.3

(a) What percentage of Utah adults are younger than 50?

(b) What percentage of Utah adults are not overweight or obese?

(c) What percentage of overweight or obese Utah adults are older than 64?

(d) What percentage of 50-64 year old Utah adults are not overweight or obese?

(e) What percentage is higher: the percentage of 18-34 year olds who are overweight or obese, or the percentage of overweight or obese adults who are 18-34 year old? Explain

Answer 1

(a) Percentage of Utah adults that are younger than 50

= 42.5 + 28.5 = 70%

(b) Percentage of Utah adults that are not overweight or obese

= 100 - Percentage of Utah adults that ars overweight or obese

= 100 - (42.5*0.411 + 28.5*0.579 + 16.4*0.682 + 12.6*0.553)

= 47.88%

(c) The required Percentage of Utah adults = (12.6*0.553)/52.12*100%

= 13.37%

(d) The required percentage of Utah adults = 100 - 68.2 = 31.8%

(e) The Percentage of 18-34 year olds who are overweight or obese = 41.1%

The Percentage of overweight or obese adults who are 18-34 year old = (42.5*0.411)/52.12*100% = 33.5%

Thus the first Percentage is higher