A test for a certain disease has a probability of 0.92 of detecting the disease when it is present anda probability of 0.08 of falsely detecting it whenit is not present. The proportion of people who are not afflicted by the disease for a givenpopulation is 70%.What is the probability that a randomly selected person from the district will test positive?

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Answered: A test for a certain disease has a…

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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2 The probability of Inspector #1 on a production line finding a defective item is 0.8 and of Inspector #2, down the line, 0.7. What is the probability of a defective item getting through?
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Light bulbs are tested for their life-span. It is found that 16% of the light bulbs are rejected. A random sample of 50 bulbs is taken from stock and tested. The random variable X is the number of bulbs that are rejected. What is the probability that the value of X is at least 5?
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When a machine is improperly adjusted, it has probability 0.15 of producing a defective item. Each day, the machine is run until three defective items are produced. When this occurs, it is stopped and checked for adjustment. What is the probability that an improperly adjusted machine will produce five or more items before being stopped? What is the average number of items an improperly adjusted machine will produce before being stopped?
It has been determined that the probability of a hurricane occuring on a certain day in a certain area is 4%. What is the probability that a hurricane does not occur on that day?
A new medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.74. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 14 % of the population who take this test have the disease.If the test administered to an individual is positive, what is the probability that the person actually has the disease?
Suppose that more than a decade ago high levels of lead in the blood put 82% of children at risk. A concerted effort was made to remove lead from the environment. Suppose, according to a survey, only 9% of children in the United States are at risk of high blood-lead levels. In a random sample of 100 children taken more than a decade ago, what is the probability that 70 or more had high blood-lead levels?
The ebola virus has an incidence rate of 15%. If the false negative is 25% and the following false positive is 30%, then find what is the conditionsl probability of an individual not having ebola, given they received a negative test result? a. 0.97 b. 0.91 c. 0.94 d. 0.88
A certain virus affects 0.7% of the population. A test used to detect the virus in a person is positive 88% of the time if the person has the virus (true positive) and 13% of the time if the person does not have the virus (false positive) Fill out the remainder of the following table and use it to answer the two questions below based on a total sample of 100,000 people. a. Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest hundredth of a percent and do not include a percent sign. b. Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest hundredth of a percent and do not include a percent sign.
Assume that a student alarm clock has a 6.6 % daily failure rate. What is the probability that the students alarm clock ill not work on the day of an important final exam?

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