Question

The Census Bureau reports that the percent of adult American females with a weight higher than what is considered healthy is 54%. We know the percent of American males with a weight higher than what is considered healthy is 46% First fill out the blank Percent Female Higher than Healthy Weight Percent Male Higher than Healthy Weight Does the assignment of probabilities for males and females over a healthy weight satisfy form a legitimate probability model? Explain why or why not? Yes/No (Provide two reasons, why or why not)

Answer 1

Yes. Reasons are :

For a probability distribution function following conditions should be satisfied

1. Each probability is positive.  

In the given example, this condition is satisfied.

2. The sum of all the probabilities for the complete support (possible values of the parameter) should be 100%

Here, the support is the males and females in the population. The probabilities for males and females with weights over the prescribed weight is 54% and 46%

The sum total is 100% which satisfies the requirement.

Thus the assignments of probabilities satisfies the legitimate probability model.