A medical test has been designed to detect the presence of a certain disease. Among people...

A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.93. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.03. It is estimated that 3% of the population who take this test have the disease. (Round your answers to three decimal places.)

(a) If the test administered to an individual is positive, what is the probability that the person actually has the disease?

(b) If an individual takes the test twice and the test is positive both times, what is the probability that the person actually has the disease? (Assume that the tests are independent.)

Expert Solution

milcah answered 1 year ago

A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease....

A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.78. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.02. It is estimated that 19 % of the population who take this test have the disease. If the test administered...

A scientist designed a medical test for a certain disease. Among 100 patients who have the...

A scientist designed a medical test for a certain disease. Among 100 patients who have the disease, the test will show the presence of the disease in 96 cases out of 100, and will fail to show the presence of the disease in the remaining 4 cases out of 100. Among those who do not have the disease, the test will erroneously show the presence of the disease in 3 cases out of 100, and will show there is no...

A certain medical test is known to detect 72% of the people who are afflicted with...

A certain medical test is known to detect 72% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

A certain medical test is known to detect 73% of the people who are afflicted with...

A certain medical test is known to detect 73% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places? Assume that 39% of people are left-handed. If we...

A certain medical test is known to detect 50% of the people who are afflicted with...

A certain medical test is known to detect 50% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

A certain medical test is known to detect 49% of the people who are afflicted with...

A certain medical test is known to detect 49% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

Suppose that a medical test for a certain disease has a sensitivity and specificity of 93%....

Suppose that a medical test for a certain disease has a sensitivity and specificity of 93%. The test is applied to a population of which 11% are actually infected by the disease. 1. Calculate the NPV and the PPV. 2. What percent of the total population will test positive who are disease-free? 3. What percent of the total population will test negative who have the disease?

Suppose that a test for a certain disease has a specificity of 95%. If 2,000 people...

Suppose that a test for a certain disease has a specificity of 95%. If 2,000 people without the disease take the test, how many should you expect to test negative? 100 1,000 1,500 1,900

A test is designed to detect cancer. If a person has cnacer, then the probability that...

A test is designed to detect cancer. If a person has cnacer, then the probability that the test will detect it is .95; if the person does not have cancer, the probability that the test will erroneously indicate that he does have cancer is .1. Assume 15% of the population who take the test have cancer. What is t he probability that a person described by the test as not having cancer really does have it?

Assume there is a medical test to diagnose a disease. If a person has the disease,...

Assume there is a medical test to diagnose a disease. If a person has the disease, the probability of having positive test result is 98 percent. If a person does not have the disease, the probability of having negative test results is 99.6 percent. The probability that a person has a disease is 1 percent in the population. Answer the following questions: a) If a person has a positive test result, what is the probability that he/she has the disease?...

Question