Question

It is estimated that approximately 10.5% of Americans are afflicted with diabetes. Suppose that a new diagnostic test is being checked for its accuracy. When the test is given to adults over 40 who have diabetes, it marks 95% positive for the disease (this is a correct diagnosis). When the test is given to adults over 40 who do not have diabetes, it marks 3.5% positive for the disease (this is an incorrect diagnosis). Round your final answers to three decimal places. (a) Find the probability that a randomly selected adult over 40 does not have diabetes, and is diagnosed as positive for diabetes by the ne

Answer 1

0.03

Explanation:

Percentage of americans with diabetes = 10.5% = 0.105

Percentage of americans without diabetes = 89.5% = 0.895

Adults over 40 with diabetes tested positive = 95% = 0.95

Adults over 40 with diabetes tested negative = 5% = 0.05

Adults over 40 without diabetes tested positive = 3.5% = 0.035

Adults over 40 without diabetes tested negative = 96.5% = 0.965

The probability of selecting an adult over 40 without diabetes but positive diagnosis;

= 0.895 * 0.035

= 0.031325

= 0.03