It is estimated that approximately 8.14% Americans are afflicted with diabetes. Supposethat a certain diagnostic evaluation for diabetes will correctly diagnose 97% of all adultsover 40 with diabetes as having the disease and incorrectly diagnoses 3.5% of all adultsover 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 havingdiabetes.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 "falsenegatives").

Given PD=8.14%=0.0814 PCD=97%=0.97 PCN=3.5%=0.035 Where D and N represent with diabetes and without…

Answered: It is estimated that approximately…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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?
What is the probability that a driver who was released had actually been drinking?
A recent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 35% in children 2-6 years of age. If 10 children are analyzed, What is the probability that five are hyperlipidemic?
Suppose that about 55% of the people who are murdered actually knew the murderer. Suppose that a detective file in Boston has 51 current unsolved murders. What is the probability that fewer than 21 victims knew their murderer?
Empirical evidence suggests that 25% of Florida drivers are uninsured. If four random Florida drivers are involved in an accident, what is the probability that more than one of them are uninsured?
A study study of the U.S. clinical population found that 22.5% are diagnosed with a mental disorder, 13.5% are diagnosed with an alcohol-related disorder, and 5% are diagnosed with both disorders. What is the probability that someone from the clinical population is diagnosed with a mental disorder, given that the person is not diagnosed with an alcohol-related disorder?
9) According to the American Academy of Ophthalmology, there is a 18% chance that someone will have hazel eyes. What is the probability that it will take at least seven people to find someone with hazel eyes?
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