It is estimated that approximately 8.14% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 97% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3.5% of all adults over 40 without diabetes as having the disease. a) Find the probability that a randomly selected adult over 40 does not have diabetes, and is diagnosed as having diabetes (such diagnoses are called "false positives"). b) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes. c) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives").

It is estimated that approximately 8.44% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 96% of all adults over 4040 with diabetes as having the disease and incorrectly diagnoses 4% of all adults over 4040 without diabetes as having the disease.     a) Find the probability that a randomly selected adult over 4040 does not have diabetes, and is diagnosed as having diabetes (such diagnoses are called "false positives").                  b) Find the probability that a randomly selected adult of 4040 is diagnosed as not having diabetes.                  c) Find the probability that a randomly selected adult over 4040 actually has diabetes, given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives").              (Note: it will be helpful to first draw an appropriate tree diagram modeling the situation)

An article was published recently suggesting that persons who exercise regularly can reduce their risk of major clinical events (e.g. diabetes, cardiovascular disease) by up to 50% in some instances. It is believed that only 30% of adult Americans exercise on a regular basis. If eight adult Americans are analyzed, what is the probability that less than half of them exercise regularly? For some reason, I keep coming out with the wrong numbers.

Bryan is performing data entry for an insurance company by taking handwritten records and entering them into the database. Thus far, 15.6% of the handwritten records have had missing data that prevented them from being entered into the database. If Bryan takes 10 handwritten records, what is the probability that at most three records will be incomplete?