Question

The following probabilities are based on data collected from U.S. adults during the National Health Interview Survey 2005-2007. Individuals are placed into a weight category based on weight, height, gender and age. Underweight Healthy Weight Overweight (Not Obese) Obese Probability 0.019 0.377 0.35 0.254 Based on this data, what is the probability that a randomly selected U.S. adult who weighs more than the healthy weight range is obese

Answer 1

The probability that a randomly selected U.S. adult who weighs more than the healthy weight range is obese is P=0.42.

Explanation:

We have the following categories and associated probabilities:

Category: Probability

Underweight: 0.019

Healthy Weight: 0.377

Overweight (Not Obese): 0.350

Obese 0.254

We have to calculate the probability that a randomly selected U.S. adult, given that weighs more than the healthy weight range, is obese.

We can calculate this as:

`P(\text{X=Ob}|\text{X=OnO or Ob})=\frac{P(\text{X=Ob})}{P(\text{X=Ob})+P(\text{X=OnO})}\\\\\\P(\text{X=Ob}|\text{X=OnO or Ob})=(0.254)/(0.350+0.254)\\\\\\P(\text{X=Ob}|\text{X=OnO or Ob})=(0.254)/(0.604)=0.42`

where:

OnO: Overweight (Not Obese)

Ob: Obese